d - l is nonsingular. Thus, we have shown that a can be written in the desired form.
To prove that a matrix a can be written as a = d - l - lt, where d is diagonal with dii > 0 for all 1 ≤ i ≤ n, l is lower triangular, and d - l is nonsingular, we need to construct such matrices d and l.
Let d be the diagonal matrix with dii = aii for all 1 ≤ i ≤ n. Then, since aii ≠ 0 for all 1 ≤ i ≤ n, we have that d is nonsingular.
Next, let l be the lower triangular matrix whose entries below the diagonal are given by li,j = -aij/dii for all 1 ≤ i < j ≤ n and whose diagonal entries are all 1. Then, we have:
d - l = [aii 0 0 ... 0 ]
[-a21/a11 a22 0 ... 0 ]
[-a31/a11 -a32/a22 a33 ... 0 ]
...
[-an1/a11 -an2/a22 -an3/a33 ... a(n-1)(n-1) ann ]
The determinant of d - l can be computed as follows:
det(d - l) = a11 (a22 ... ann - 0 ... 0) +
a21 (-a32 ... ann - 0 ... 0) +
a31 (a32 ... ann - 0 ... 0) +
...
an1 ((-1)^(n-1) a(n-1)(n-1) ... a22) != 0
Therefore, d - l is nonsingular. Thus, we have shown that a can be written in the desired form.
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HELP I NEED HELP ASAP
Answer:
constant... I think... sorry if it's wrong... just trying to help ;-;
Step-by-step explanation:
Hope this helped! Good luck! :)
Answer:
linear
Step-by-step explanation:
if you put it into an equation, it would be y = 5 + 2x, which is a linear (straight line) equation
Exercice 1:
Voici un programme de calcul :
Choisir un nombre
Multiplier ce nombre par 4
Ajouter 8
Multiplier le résultat par 2
1. Vérifier que si on choisit le nombre -0,5, ce programme donne 12 comme résultat final.
2. Le programme donne 34 comme résultat final, quel est le nombre choisi au départ ?
Dans la suite de l'exercice, on nomme x le nombre choisi au départ.
3. L'expression A = 2(4x + 8) donne le résultat du programme de calcul précédent pour un nombre x
donné.
On pose B = (4 + x)2 – x2
Prouver que les expressions A et B sont égales pour toutes les valeurs de x.
4. Pour chacune des affirmations suivantes, indiquer si elle est vraie ou fausse.
On rappelle que les réponses doivent être justifiées.
Affirmation 1: Ce programme donne un résultat positif pour toutes les valeurs de x.
Affirmation 2 : Si le nombre x choisi est un nombre entier, le résultat obtenu est un multiple de 8.
Mr. Hartman, the school librarian, is ordering new keyboards and mice for all of the school's computer labs. Each keyboard costs $13.50, and each mouse costs $6.50. There are 3 computer labs in the school, and each computer lab has s computer stations. Pick all the expressions that represent how much Mr. Hartman will spend on new keyboards and mice.
Answer:
3 * 20s
Step-by-step explanation:
In order to find out how much Mr. Hartman will spend in total we first need to multiply the price of the keyboard and mouse by the number of computers in a single computer station. Once we have these products we add them together. Finally, we multiply this new value by 3 since there are a total of 3 computer stations. If we turn this into an expression it would be the following...
3 * (13.50s + 6.50s)
We can even simplify this by first adding the cost of the keyboard and mouse and then multiplying by s
3 * 20s
The sale price of a model railroad set is $174. If it was marked down to 25% off of the original price, what was the original price?
Answer:
$217.50
Step-by-step explanation:
I) Make an equation to find the answer:
o = s + 0.25s (original price = sale price + 25% of sale price)
II) Solve:
o = 174 + 0.25(174)
o = 217.50
If the price was 174 after the mark down of 25%, then adding 25% back will give you the answer.
174 + 25% (which is 43.5) = $217.5
Hope this helps!
A right triangle has side lengths,8,15,17 and as shown below.
Use these lengths to find, tan b, cos b, sin b
Remember the chant "soh cah toa"
sine = opposite ÷ hypotheneus
cosine = adjacent ÷ hypotheneus
tangent = opposite ÷ adjacent
remember that hypotheneus is the slanty side, opposite and adjacent side is in COMPARISON with the angle you want to find.
In this case, tan B would be 15/8
sinB = 15/17
cosB = 8/17
in a unit circle, what is the relationship between arc length and central angle?
Answer:
The measure of an arc refers to the arc length divided by the radius if the circle. The arc measure equals the corresponding central angle measure, in radians.
can someone please help me with thiss!?
I would first find the volume of the hole and multiply that by 2 because there's 2 holes.
[tex]v = lwh[/tex]
[tex]v = (5)(8)(5)[/tex]
[tex]v = 200[/tex]
[tex]200 \times 2 = 400[/tex]
//
I would then find the volume of the entire cinder block.
[tex]v = lwh[/tex]
[tex]v = (16)(8)(8)[/tex]
[tex]v = 1024[/tex]
//
I would then substract.
[tex]1024 - 400 = 624[/tex]
The volume of the cinder blocks is 624 inches³
mid-segment definition
Answer:
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.
Step-by-step explanation:
hope this helps :)
What is the value of (Negative one-half)–4?
-16
Negative StartFraction 1 Over 16 EndFraction
StartFraction 1 Over 16 EndFraction
16
Answer: D
The answer is D, 16
Answer:
D is correct.
Step-by-step explanation:
welcome have a good day.
The height of a doorway is 7 yards. What is the height of the doorway in inches?
The height of the doorway is ____ inches.
What is the equation of this line?
Answer:
y = -x +2
Hope that helps
Select the correct answer.
Which equation shows function g in factored form?
[tex]g(x)=2x^2-6x-56[/tex]
A.
g(x) = 2(x2 − 3x − 28)
B.
g(x) = 2(x − 4)(x + 7)
C.
g(x) = (2x + 7)(x − 8)
D.
g(x) = 2(x + 4)(x − 7)
Answer:
The answer is A.
[tex]g(x) = 2( {x}^{2} - 3x - 28)[/tex]
Answer:
Have a great rest of your day :)
Step-by-step explanation:
Marie is saving $75 each week so she can buy a new laptop which costs $1200. She has already saved $125. Find the minimum number of weeks she will have to save in order to be able to make this purchase.
Answer:
Step-by-step explanation:
[tex]125+75w\ge 1200\\ \\ 75w\ge 1075\\ \\ w\ge 14.33\\ \\ \text{So she must save for at least 15 weeks.}[/tex]
If anyone could answer any of these that would be awesome
Answer:
10
Step-by-step explanation:
12.)
m = -2 n = -3
Evaluate: m(m + n)
Substitute!
-2(-2 + -3)
Do the parenthesis
-2(-2 -3)
(-2)(-5)
= 10
I hoped this helped
Name the Property:
Associative Property, Distributive
Property, Identity Property of
Multiplication
13. ax 1 =a
Answer:
Property of Multiplication
Step-by-step explanation:
hope this helps
Question 1 of 10
What is the area of the rectangle below?
J
8
15
A. 23 sq. units
B. 120 sq. units
C.46 sq.units
D.60 sq.units
Area of rectangle
L × B
8 × 15
15
×8
= 120 sq units
Calculate the simple interest on $ 6400 at 10% p.a. for 9 months.
Step-by-step explanation:
SI=P×T×R÷100
SI= 6400×9×10÷100
SI=576000÷100
SI=5760
Question 3
This table shows a linear relationship between the amount of water in a tank and time.
Time (minutes) Water (gallons)
0 30
5 20
10 10
Which of these statements is true?
Multiple choice question.
A)
The water in the tank is increasing at a rate of 2 gallons per minute.
B)
The water in the tank is increasing at a rate of 10 gallons per minute.
C)
The water in the tank is decreasing at a rate of 2 gallons per minute.
D)
The water in the tank is decreasing at a rate of 10 gallons per minute.
Answer:
C
Step-by-step explanation:
In five minutes it decreased by 10 gallons (5x2=10), In 10 minutes it decreased by 20 gallons.
The spinner below is spun. Find the probability,
P(D greater than 1)
What is the numerator for the probability?
What is the denominator for the probability?
Answer:
5 - numerator
6 - denominator
John makes 2 cookies a day. Write an equation that shows the relationship between the days and number of cookes John
makes. Write an equation
Answer:
2x
x = each day
Step-by-step explanation:
Answer:
y= 2(x)
Step-by-step explanation:
The Y is the cookies. X is the days. Every day that John bakes, he makes 2 cookies. So you multiply the days by 2 to find the number of cookies he bakes.
SOMEBODY PLEASE HELP ASAP PLEASE PLEASE PLEASE WILL GIVE YOU A GIFTCARD OF YOUR CHOICE
Answer:
what grade are u in
Step-by-step explanation:
Answer: I hope this helps!! It would mean the world to me if i got an Amazon or Xbox giftcard thanks!! :D
Step-by-step explanation:
PLA HURRY I WILL GIVE BRAINLIST
Answer:
last one? if not i tried
Step-by-step explanation:
find compound interest on12600rupees for 2years at10% per annum compounded anually
Answer:
₹2520
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 10%/100 = 0.1 per year,
then, solving our equation
I = 12600 × 0.1 × 2 = 2520
I = ₹ 2,520.00
The simple interest accumulated
on a principal of ₹ 12,600.00
at a rate of 10% per year
for 2 years is ₹ 2,520.00.
Mitchell went to the grocery store and bought 30 bagels. If there are 3 bagels in each pack, how many packs of bagels did Mitchell buy?
Answer: 10
Step-by-step explanation: 30/3=10
Answer:
10
Step-by-step explanation:
Take the total number of bagels and divide by the number of bagels per package to determine the number of packs
30/3 = 10
He will buy 10 packs
(100 POINTS!!) Help me on this please! (I will mark you brainliest!)
Answer:
its the 3rd and 5th check mark
Step-by-step explanation:
It is the 3rd and 5th answer check mark thingy!
Hope this helped, thanks so much for the points :)
13.
Find the slope of the line.
A. -7
B. 1/7
C. -1/7
D. 7
Answer:
[tex]\displaystyle m=\frac{1}{7}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a Cartesian planeCoordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-2, 2)
Point (5, 3)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m=\frac{3-2}{5+2}[/tex][Fraction] Subtract/Add: [tex]\displaystyle m=\frac{1}{7}[/tex]The mall is having a sale on all shoes. Each pair is $3.50 off the original price. Which expression shows the final price of a pair of shoes?
3.5+x
x- 3.5
3.5x
which is the answer???
and could anybody help me with a few more questions?
Answer:
x-3.5
Step-by-step explanation:
I suppose that x= the orginal cost of the pairs of shoes.
The expression that shows the final price of a pair of shoes is given by f(x) = (x - 3.5).
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the mall is having a sale on all shoes. Each pair is $3.50 off the original price.
Assume the original price of the shoes is $x. So, the expression that shows the final price of a pair of shoes is given by -
f(x) = (x - 3.5)
Therefore, the expression that shows the final price of a pair of shoes is given by f(x) = (x - 3.5).
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Can you find the midpoint of the segment with the following endpoints.
(-7,-5) and (-4,2)
9514 1404 393
Answer:
(-5.5, -1.5)
Step-by-step explanation:
The midpoint is the average of the end points:
((-7, -5) +(-4, 2))/2 = (-7-4, -5+2)/2 = (-11, -3)/2 = (-5.5, -1.5)
The midpoint of the segment is (-5.5, -1.5).
Altogether, 360 schoolchildren sit down for their exams.
Five percent of them have one pen. Of the remaining 95
percent, half of them have two pens and the other half
have none. How many pens do the children have between
all of them?
HEL MEEEE
Answer:
A esta así no puedo xd ._.
Total Pens, owned by all students between all of them = 360
Percentage wise calculation of Pens
Total children = 360
Students having one pen = 95% of 360 = 18
Remaining 95% = 360 - 18 = 342
Half of remaining ie 342 = 171, have two pens
Other half of remaining ie 171 have no pens
Total pens, all children have between all of them = Summation (number of students x number of pens)
= (18 x 1) + (171 x 2) + (171 x 0)
= 18 + 342
= 360
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4^x. 2^y =128,find x and y .please needed urgently