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Vectors and matrices — Question 6

QCAA 2020, Paper 2 · 1 mark

Q6 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 6

Solve the matrix equation for

\mathbf X

.

\begin{bmatrix}0&1\\2&3\end{bmatrix}\mathbf X\begin{bmatrix}4&5\\6&7\end{bmatrix}=\begin{bmatrix}8&9\\0&1\end{bmatrix}

.

(A)

\begin{bmatrix}-9&-9\\4&4\end{bmatrix}

(B)

\begin{bmatrix}3&-4\\-1&2\end{bmatrix}

(C)

\begin{bmatrix}13&-14\\-11&12\end{bmatrix}

(D)

\begin{bmatrix}54&56\\-28&-29\end{bmatrix}

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

B

Worked solution

If

A X B=C

, then

X=A^{-1}CB^{-1}

. Using the two inverse matrices gives

X=\begin{bmatrix}3&-4\\-1&2\end{bmatrix}

.

Selects option B.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

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