Question

5

Answer 1

The value of the matrix X is $X = \left[\begin{array}{cc}0.5&0\\1&-0.5\end{array}\right]$

How to solve for matrix X?

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The given matrices are:

$A = \left[\begin{array}{cc}5&-3\\4&-2\end{array}\right]$

$B = \left[\begin{array}{cc}-1&1\\0&2\end{array}\right]$

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

The expression is given as:

A(X - B) = C

Expand

AX - BX = C

This gives

$\left[\begin{array}{cc}5&-3\\4&-2\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] - \left[\begin{array}{cc}-1&1\\0&2\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}-1&2\\-2&2\end{array}\right]$

Evaluate the products

$\left[\begin{array}{cc}5a - 3c&5b -3d\\4a - 2c&4b -2d\end{array}\right] - \left[\begin{array}{cc}-a + c&-b + d\\2c&2d\end{array}\right] = \left[\begin{array}{cc}-1&2\\-2&2\end{array}\right]$

Evaluate the difference

$\left[\begin{array}{cc}6a - 4c&6b -4d\\4a - 4c&4b -4d\end{array}\right] = \left[\begin{array}{cc}-1&2\\-2&2\end{array}\right]$

By comparing the positions, we have:

6a - 4c = -1

6b - 4d = 2

4a - 4c = -2

4b - 4d = 2

Rewrite as:

6a - 4c = -1 and 4a - 4c = -2

6b - 4d = 2 and 4b - 4d = 2

Using a graphing tool, we have:

a = 0.5, c = 1, b = 0, and d = -0.5

Hence, the matrix X is:

$X = \left[\begin{array}{cc}0.5&0\\1&-0.5\end{array}\right]$

Read more about matrices at:

brainly.com/question/11989522

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