Given the matrices A = \begin{pmatrix} 2 & 3 \\ 1 & m \end{pmatrix} and B = \begin{pmatrix… — JAMB UTME

Given the matrices $A = \begin{pmatrix} 2 & 3 \\ 1 & m \end{pmatrix}$ and $B = \begin{pmatrix} 4 \\ -2 \end{pmatrix}$ , if the matrix product $AB = \begin{pmatrix} 2 \\ 6 \end{pmatrix}$ , what is the value of $m$ ?

$-1$ Answer
B
$1$
C
$-3$
D
$-5$

Answer

The value of

m

-1

Multiplying the

2 \times 2

matrix by the

2 \times 1

column vector yields a

2 \times 1

result where the second row entry is

1(4) + m(-2) = 4 - 2m

. Setting this equal to the second row element

6

gives

4 - 2m = 6

, which simplifies to

m = -1

Step-by-Step Solution

Compute the matrix product

AB

AB = \begin{pmatrix} 2(4) + 3(-2) \\ 1(4) + m(-2) \end{pmatrix} = \begin{pmatrix} 8 - 6 \\ 4 - 2m \end{pmatrix} = \begin{pmatrix} 2 \\ 4 - 2m \end{pmatrix}

Matrix multiplication requires taking the dot product of each row of the first matrix with the column vector.

Equate the resulting vector to the given vector

\begin{pmatrix} 2 \\ 6 \end{pmatrix}

4 - 2m = 6

Corresponding elements of equal matrices must be equal.

Solve the linear equation for

m

-2m = 6 - 4 \Rightarrow -2m = 2 \Rightarrow m = -1

Isolating the variable

m

by subtracting

4

from both sides and dividing by

-2

Key Concept

Matrix Multiplication and Equality of Matrices

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