If A = {pmatrix}3 & 2 & 1\\4 & 2 & -1{pmatrix} and B = {pmatrix}1 & 4\\0 & 1\\3 & 2{pmatrix}. Find A^T + B, ( where T means transpose)

Correct Answer is : (482341){pmatrix}4 & 8\\2 & 3\\4 & 1{pmatrix}424831

{pmatrix}4 & 8\\3 & 2\\4 & 1{pmatrix}

{pmatrix}4 & -8\\3 & 2\\4 & 1{pmatrix}

{pmatrix}4 & 8\\4 & -2\\3 & 1{pmatrix}

{pmatrix}4 & 8\\2 & 3\\4 & 1{pmatrix}

Correct Answer is : (482341){pmatrix}4 & 8\\2 & 3\\4 & 1{pmatrix}424831

Test Index

JAMB Mathematics 2024 Paper

Question : 44

Total: 50

If A =

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

\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}

^T

+ B, ( where T means transpose)

Solution:

Concept:

Transposing matrix A swaps its rows and columns, then you add corresponding elements of matrices of the same order.

Explanation:

The transpose of A is formed by turning each column of A into a row.

A^T = \begin{pmatrix}3 & 4\\2 & 2\\1 & -1\end{pmatrix}

Both

A^T

and B are

3 \times 2

matrices, so they can be added entry by entry.

Row 1:

3+1=4

4+4=8

Row 2:

2+0=2

2+1=3

Row 3:

1+3=4

-1+2=1

Thus

A^T + B = \begin{pmatrix}4 & 8\\2 & 3\\4 & 1\end{pmatrix}

Answer:

Option D:

\begin{pmatrix}4 & 8\\2 & 3\\4 & 1\end{pmatrix}

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