If P = \begin{pmatrix} 3 & 1 \\ 2 & 4 \end{pmatrix} and Q = \begin{pmatrix} 1 & -2 \\ 0 & … — JAMB UTME

If $P = \begin{pmatrix} 3 & 1 \\ 2 & 4 \end{pmatrix}$ and $Q = \begin{pmatrix} 1 & -2 \\ 0 & 5 \end{pmatrix}$ , what is the product matrix $PQ$ ?

The product matrix

PQ

\begin{pmatrix} 3 & -1 \\ 2 & 16 \end{pmatrix}

The matrix containing elements 3, -1 in the top row and 2, 16 in the bottom row correctly applies the row-by-column multiplication rule for matrices

P

and

Q

Set up the row-by-column matrix multiplication

PQ

PQ = \begin{pmatrix} 3 & 1 \\ 2 & 4 \end{pmatrix} \begin{pmatrix} 1 & -2 \\ 0 & 5 \end{pmatrix}

Matrix multiplication requires computing dot products of rows of the first matrix with columns of the second matrix.

Calculate the first row elements of the product matrix

Row 1, Column 1:

3(1) + 1(0) = 3 + 0 = 3

; Row 1, Column 2:

3(-2) + 1(5) = -6 + 5 = -1

Multiply elements of Row 1 of

P

by corresponding elements of Columns 1 and 2 of

Q

and sum them.

Calculate the second row elements of the product matrix

Row 2, Column 1:

2(1) + 4(0) = 2 + 0 = 2

; Row 2, Column 2:

2(-2) + 4(5) = -4 + 20 = 16

Multiply elements of Row 2 of

P

by corresponding elements of Columns 1 and 2 of

Q

and sum them.

Assemble the resulting

2 \times 2

matrix

PQ = \begin{pmatrix} 3 & -1 \\ 2 & 16 \end{pmatrix}

Combine all computed entry values into matrix form.

Matrix Multiplication (Row-by-Column Rule)

Tahmini Süre:1m 30s

Soru