Solve the matrix equation for $a,\ b,\ c,$a, b, c, and $d$d .$\begin{bmatrix}a&b\\3&-4\end{bmatrix}=\begin{bmatrix}6&2\\c&d\end{bmatrix}$[a b3 −4]=[6 2c d]$a=$a= , $b=$b= , $c=$c= , $d=$d=

Question

Solve the matrix equation for $a,\ b,\ c,$ a, b, c, and $d$ d . $\begin{bmatrix}a&b\\3&-4\end{bmatrix}=\begin{bmatrix}6&2\\c&d\end{bmatrix}$ [a b3 −4]=[6 2c d] $a=$ a= , $b=$ b= , $c=$ c= , $d=$ d=

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Solution

The given matrix equation is:

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

We can equate the corresponding elements of the two matrices to solve for $a, b, c,$ and $d$ .

From the first row and first column, we get $a = 6$ .

From the first row and second column, we get $b = 2$ .

From the second row and first column, we get $3 = c$ .

From the second row and second column, we get $-4 = d$ .

So, the solution to the matrix equation is $a = 6, b = 2, c = 3,$ and $d = -4$ .

This problem has been solved

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