Question

2. What is the solution of matrix equation
[2 7
1 4] x=[2 5]

Answer 1

(d) X = [-27, 8]

Explanation:

The solution to the matrix equation can be found by left-multiplying both sides of the equation by the inverse of the coefficient matrix.

AX = B . . . . given

X = A⁻¹B

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`X=\left[\begin{array}{cc}2&7\\1&4\end{array}\right]^(-1)\left[\begin{array}{c}2\\5\end{array}\right] =\left[\begin{array}{cc}4&-7\\-1&2\end{array}\right]\left[\begin{array}{c}2\\5\end{array}\right] \\\\X=\left[\begin{array}{c}-27\\8\end{array}\right]`

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Additional comment

A calculator or spreadsheet can help with this. The solution can also be found by row-reducing the augmented matrix.