Question

solve the matrix equation [4] X = [–4 8]
[1 ] [–1 2]

Answer 1

Complete question:

Solve the matrix equation $\left[\begin{array}{c}4\\1&\end{array}\right]$.X = $\left[\begin{array}{cc}-4&8\\-1&2\end{array}\right]$

The matrix X = $\left[\begin{array}{cc}-1&2\end{array}\right]$

Given:

Matrix equation $\left[\begin{array}{c}4\\1&\end{array}\right]$.X = $\left[\begin{array}{cc}-4&8\\-1&2\end{array}\right]$

To Find:

X =?

Solution:

Let matrix X = $\left[\begin{array}{cc}x&y\end{array}\right]$

Since  $\left[\begin{array}{c}4\\1&\end{array}\right]$.$\left[\begin{array}{cc}x&y\end{array}\right]$ = $\left[\begin{array}{cc}-4&8\\-1&2\end{array}\right]$

⇒ $\left[\begin{array}{cc}4x&4y\\x&y\end{array}\right]$ = $\left[\begin{array}{cc}-4&8\\-1&2\end{array}\right]$

Comparing both sides, we get

4x = -4 and 4y = 8

x = -1 and y = 2

Hence, the matrix X = $\left[\begin{array}{cc}-1&2\end{array}\right]$

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