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Exam-Style Questions on MatricesProblems on Matrices adapted from questions set in previous Mathematics exams. |
1. | IB Standard |
Let \(A\) = \( \begin{pmatrix} 1 & 3 & 2 \\ 3 & 0 & 1 \\ 1 & 1 & 2 \\ \end{pmatrix} \) and \(B\) = \( \begin{pmatrix} 7 \\ 7 \\ 5 \\ \end{pmatrix} \)
(a) Write down \(A^{-1}\)
(b) Find \(X\) if \(AX=B\)
2. | IB Standard |
If the equations below can be represented as the matrix equation \(AX=B\), where \(X=\begin{pmatrix}x\\y\\z\end{pmatrix}\)
$$x-2y-z=2$$ $$x+y=1$$ $$-2x+y-3z=-23$$(a) What is the matrix \(A\) ?
(b) What is the matrix \(B\) ?
(c) Find the matrix \(A^{-1}\).
(d) Use your answers to the previous three parts of this question to find the values of \(x,y\) and \(z\).
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