Given matrix M ={vmatrix} -2 & 0 & 4 \\ 0 & -1 & 6 \\ 5 & 6 & 3 {vmatrix}, findM^{T} + 2M

Correct Answer is : ∣−60130−31814189∣{vmatrix} -6 & 0 & 13 \\ 0 & -3 & 18 \\ 14 & 18 & 9 {vmatrix}−60140−31813189

{vmatrix} -4 & 2 & 1 \\ 6 & 0 & 5 \\ 0 & 6 & 2 {vmatrix}

{vmatrix} -6 & 0 & 13 \\ 0 & -3 & 18 \\ 14 & 18 & 9 {vmatrix}

{vmatrix} 5 & 2 & 6 \\ 0 & 1 & 1 \\ 3 & 4 & -7 {vmatrix}

{vmatrix} -4 & 0 & 8 \\ 0 & -2 & -16 \\ 10 & 12 & 6 {vmatrix}

Correct Answer is : ∣−60130−31814189∣{vmatrix} -6 & 0 & 13 \\ 0 & -3 & 18 \\ 14 & 18 & 9 {vmatrix}−60140−31813189

Test Index

JAMB Mathematics 2019 Paper

Question : 13

Total: 73

Given matrix M =

\begin{vmatrix} -2 & 0 & 4 \\ 0 & -1 & 6 \\ 5 & 6 & 3 \end{vmatrix}

M^{T} + 2M

Solution:

Concept:

Find the transpose of matrix

M

, multiply

M

2

, then add the two resulting matrices.

Explanation:

First, write the transpose

M^T

by swapping rows and columns.

M^T = \begin{vmatrix} -2 & 0 & 5 \\ 0 & -1 & 6 \\ 4 & 6 & 3 \end{vmatrix}

Next, multiply every element of

M

2

to get

2M

2M = \begin{vmatrix} -4 & 0 & 8 \\ 0 & -2 & 12 \\ 10 & 12 & 6 \end{vmatrix}

Now add the corresponding elements of

M^T

and

2M

M^T + 2M = \begin{vmatrix} -2-4 & 0+0 & 5+8 \\ 0+0 & -1-2 & 6+12 \\ 4+10 & 6+12 & 3+6 \end{vmatrix}

M^T + 2M = \begin{vmatrix} -6 & 0 & 13 \\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}

Answer:

M^T + 2M = \begin{vmatrix} -6 & 0 & 13 \\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}

This matches option B.

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