Solving a 3×3 System Using Technology

00:00 4 marks

A 3×3 linear system is given by the matrix equation \(AX = B\), where
\(A = \begin{pmatrix} 2 & -1 & 3 \\ 0 & 4 & 1 \\ -2 & 5 & -3 \end{pmatrix}\) and \(B = \begin{pmatrix} 5 \\ 6 \\ -4 \end{pmatrix}\).

Using a calculator or graphing software, determine the vector \(X\) that satisfies the equation.

Show all steps and justify your answer.

Hint Hint

Hint

Recall the process of finding the inverse of a matrix using your calculator and multiply it with B.

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Answer Answer

Complete Answer

The solution vector is \(X = \begin{pmatrix} -15.75 \\ -0.5 \\ -14 \end{pmatrix} = \begin{pmatrix} -\frac{63}{4} \\ -\frac{1}{2} \\ -14 \end{pmatrix}\).

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