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Matrices and Determinants - SS3 Mathematics Past Questions and Answers - page 1

1

Let \(A = \begin{bmatrix} 2 & - 4 & 3 \\ 5 & 1 & 0 \\ \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 4 & - 2 \\ - 3 & 3 & - 1 \\ \end{bmatrix}\). Find \(B - A\)

A

\[\begin{bmatrix} - 1 & 8 & - 5 \\ - 8 & 2 & - 1 \\ \end{bmatrix}\]

B

\[\begin{bmatrix} - 1 & 4 & 5 \\ 8 & 2 & - 1 \\ \end{bmatrix}\]

C

\[\begin{bmatrix} 1 & 8 & 5 \\ 8 & 2 & 1 \\ \end{bmatrix}\]

D

\[\begin{bmatrix} 2 & 4 & 1 \\ 0 & 6 & 3 \\ \end{bmatrix}\]

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2

Let \(A = \begin{bmatrix} 1 & 4 \\ 2 & 3 \\ \end{bmatrix}\), \(B = \begin{bmatrix} 0 & - 3 \\ 5 & 1 \\ \end{bmatrix}\) and \(C = \begin{bmatrix} 1 & 2 \\ 6 & - 1 \\ \end{bmatrix}\). Find \(2A - 3B + C\)

A

\(\begin{bmatrix} 8 & 28 \\ 4 & 0 \\ \end{bmatrix}\)

B

\(\begin{bmatrix} 3 & 19 \\ - 5 & 2 \\ \end{bmatrix}\)

C

\(\begin{bmatrix} 2 & - 7 \\ - 7 & 3 \\ \end{bmatrix}\)

D

\(\begin{bmatrix} 4 & 16 \\ 8 & - 8 \\ \end{bmatrix}\)

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3

Let \(A = \begin{bmatrix} 2 & 3 \\ 0 & - 2 \\ 4 & 5 \\ \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 3 & 2 \\ - 1 & 0 & 6 \\ \end{bmatrix}\). Find \(BA\)

A

\(\begin{bmatrix} 10 & 7 \\ 22 & 27 \\ \end{bmatrix}\)

B

\(\begin{bmatrix} 3 & 6 \\ 3 & 0 \\ \end{bmatrix}\)

C

\(\begin{bmatrix} 5 & 12 \\ 11 & 5 \\ \end{bmatrix}\)

D

\(\begin{bmatrix} 9 & 0 \\ - 1 & 5 \\ \end{bmatrix}\)

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4

If \(A = \begin{bmatrix} 1 & 0 \\ 2 & 2 \\ 11 & 5 \\ 4 & - 6 \\ \end{bmatrix}\), find \(A^{T}\)

A

\(\begin{bmatrix} 1 & 0 \\ 2 & 2 \\ 11 & 5 \\ 4 & - 6 \\ \end{bmatrix}\)

B

\(\begin{bmatrix} 0 & 2 & 5 & - 6 \\ 1 & 2 & 11 & 4 \\ \end{bmatrix}\)

C

\(\begin{bmatrix} 1 & 11 \\ 2 & - 6 \\ \end{bmatrix}\)

D

\(\begin{bmatrix} 2 & 2 \\ 11 & 5 \\ \end{bmatrix}\)

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5

Let \(A = \begin{bmatrix} 7 & 3 \\ 4 & 2 \\ \end{bmatrix}\) and \(B = \begin{bmatrix} - 3 & 1 \\ 2 & 4 \\ \end{bmatrix}\), find \(|A| + |B|\)

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6

Evaluate \(|B| = \left| \begin{matrix} 2 & 3 & - 4 \\ 1 & 2 & 3 \\ 3 & - 1 & - 1 \\ \end{matrix} \right|\)

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7

Using determinant method to solve the simultaneous equations: \(2x + 3y = - 2\) and \(3x + 4y = - 6\)

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