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3 years ago

The table below represents a linear relationship.

Mathematics

2 answers:

Travka [436]3 years ago

3 0

Answer:

-2

Step-by-step explanation:

the slope is 1/3

so subtract 3 fron fhe y side of the table and 1 from the x side of the table

Alex3 years ago

3 0

-2
It’s because the slope is 1/3
What you do is you subtract 3 from the y side of the table and 1 from the x side

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[10 points] Given matrix A =  2 2 3, −6 −7 8 (a) (5 points). Show that A has no LU decomposition. (b) (5 points). Find the dec

ch4aika [34]

Answer:

Both the answers are as in the solution.

Step-by-step explanation:

As the given matrix is not in the readable form, a similar question is found online and the solution of which is attached herewith.

Part a:

Given matrix is : A = $\left[\begin{array}{ccc}0&3&4\\1&2&3\\-3&-7&8\end{array}\right]$

Here,

$det(A) =\left|\begin{array}{ccc}0&3&4\\1&2&3\\-3&-7&8\end{array}\right| = -55 \neq 0.$

Then, A is non-singular matrix.

Here, A₁₁= 0.

If we write A as LU with L lower triangular matrix and U upper triangular matrix, then A₁₁=L₁₁U₁₁.

So, As

A₁₁ = 0 gives L₁₁U₁₁= 0 ,

This indicates that either L₁₁= 0 or U₁₁ = 0.

If L₁₁= 0 or U₁₁ = 0, this would made the corresponding matrix singular, which contradicts the condition as A is non-singular.

Therefore, A has no LU decomposition.

Part b:

By the implementation of the various row operations

interchange R1 and R2

$\left[\begin{array}{ccc}1&2&3\\0&3&4\\-3&-7&8\end{array}\right]$

R3+3R1=R3

$\left[\begin{array}{ccc}1&2&3\\0&3&4\\0&-1&17\end{array}\right]$

R3+(1/3)R2 = R3

$\left[\begin{array}{ccc}1&2&3\\0&3&4\\0&0&55/3\end{array}\right]$

Therefore, U = $\left[\begin{array}{ccc}1&2&3\\0&3&4\\0&0&55/3\end{array}\right]$ .

Here, LP = E₁₂=E₃₁=-3 &E₃₂=-1/3

$LP=\left[\begin{array}{ccc}0&1&0\\1&0&0\\0&0&1\end{array}\right] \left[\begin{array}{ccc}1&0&0\\0&1&0\\-3&0&1\end{array}\right]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&-1/3&1\end{array}\right]$

$LP=\left[\begin{array}{ccc}0&1&0\\1&0&0\\-3&-1/3&1\end{array}\right]$

$LP=\left[\begin{array}{ccc}1&0&0\\0&1&0\\-1/3&-3&1\end{array}\right]\left[\begin{array}{ccc}0&1&0\\1&0&0\\0&0&1\end{array}\right]$

So now U is given as

$U=\left[\begin{array}{ccc}1&2&3\\0&3&4\\0&0&55/3\end{array}\right]\\L=\left[\begin{array}{ccc}1&0&0\\0&1&0\\-1/3&-3&1\end{array}\right]\\P=\left[\begin{array}{ccc}0&1&0\\1&0&0\\0&0&1\end{array}\right]\\$

4 0

3 years ago

Lines l and m are parallel. If m1 = 126, how many degrees is m2?

VashaNatasha [74]

The answer is: " 54 ° " .

____________________________

→ The m∠2 {"measure of angle 2"} in the figure shown is: " 54 ° " .

____________________________

Explanation:

____________________________

In the figure shown in the "image attached" :

∠1 and ∠2 are "consecutive exterior angles" ;

and: "consecutive exterior angles" are "supplementary" ;

→ which means that their measurements add up to " 180° " .

____________________________

So: Given: " m∠1 = 126 " ;

We are asked to find: " m∠2 " .

→ {the measure of "angle 2" }.

____________________________

To solve:

____________________________

→ " m∠2" = 180 − ( m∠1 ) ;

= 180 − ( 126 ) ;

= 54 .

____________________________

The answer is: " 54 ° " .

____________________________

The m∠2 {"measure of angle 2"} in the figure shown is: " 54 ° " .

____________________________

4 0

4 years ago

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the surface area of a square pyramid is 84 square inches. the side length of the base is 6 inches. what is the value of x?

Sladkaya [172]

The formula is(V=B•h)(84•6)

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4 years ago

goldfiish [28.3K]

Answer:

See below

Step-by-step explanation:

It is very simple, just multiply the principal amount by the interest rate:

a: 2500 x 0.018 = £45

b: 2500 x 0.021 = £52.50

c: 2500 x 0.024 = £60

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3 years ago

Miranda has 180 beads for making helpers. She buys 240 more beads. She wants to store the beads in a case with 6 sections. how m

yuradex [85]

Answer:

70 is the answer.

Step-by-step explanation:

180+240= 420

420 divided by 6 is 70

4 0

3 years ago