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Schach [20]
2 years ago
6

Can someone help me please

Mathematics
1 answer:
Misha Larkins [42]2 years ago
4 0

Answer:

-28

Step-by-step explanation:

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Given: A, B, and C What is the value of X in the matrix equation AX + B = C?
Ksju [112]

Answer:

Option (2)

Step-by-step explanation:

Given expression is, AX + B = C

A=\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}

B=\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}

C=\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}

AX + B = C

AX = C - B

C - B = \begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}-\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix} = \begin{bmatrix}-42+7 & -20+9\\ 5-4 & 4+1\end{bmatrix}

C - B = \begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}

Let  X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}

AX = \begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}\times \begin{bmatrix}a & b\\ c & d\end{bmatrix}

     = \begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}

Since AX = C - B

\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}=\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}

Therefore, a = 1, b = 5

(-3a - 4c) = -35

3(1) + 4c = 35

3 + 4c = 35

4c = 32

c = 8

And (-3b - 4d) = -11

3(5) + 4d = 11

4d = -4

d = -1

Therefore, Option (2). X = \begin{bmatrix}1 & 5\\ 8 & -1\end{bmatrix} will be the answer.

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The perimeter of a rectangular field is 364 yards. If the width of the field is 84 yards, what is its length?


(364 : 2) - 84 =

182 - 84 =

98



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