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  • Find the matrix A such that <img alt="A\begin{bmatrix} 1 &2 \\ -1& 0 \end{bmatrix}= \begin{bmatrix} 3 &4 \\ -1&6 \end{bmatrix}" src="https://entrancecorner.codecogs.com/gif.latex?A%5Cbegin%7Bbmatrix%7D%201%20%262%20%5C%5C%20-1%26%2

Find the matrix A such that A\begin{bmatrix} 1 &2 \\ -1& 0 \end{bmatrix}= \begin{bmatrix} 3 &4 \\ -1&6 \end{bmatrix}

 

 

Answers (1)

Given:

A\begin{bmatrix} 1 &2 \\ -1& 0 \end{bmatrix}= \begin{bmatrix} 3 &4 \\ -1&6 \end{bmatrix}

Let 

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

\begin{bmatrix} a &b \\ c& d \end{bmatrix}\begin{bmatrix} 1 &2 \\ -1& 0 \end{bmatrix}= \begin{bmatrix} 3 &4 \\ -1&6 \end{bmatrix}

\begin{bmatrix} a-b &2a \\ c-d& 2c \end{bmatrix}= \begin{bmatrix} 3 &4 \\ -1&6 \end{bmatrix}

2a = 4  => a =2

a-b = 3  => b=-1

2c = 6   => c = 3

c-d = -1  => d = 4

A = \begin{bmatrix} 2 &-1 \\ 3& 4 \end{bmatrix}

Posted by

Safeer PP

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