Given P = 4 & 3 1 & 2 , then P2 = P x P.

Question

ScanSolve AI Tutor · Accepted Answer

Here's the solution for question 5 b) i):

To calculate $P^2$ , we multiply matrix $P$ by itself.

Write out the matrix multiplication.
Given $P = \begin{pmatrix} 4 & 3 \\ 1 & 2 \end{pmatrix}$ , then $P^2 = P \times P$ .
$P^2 = \begin{pmatrix} 4 & 3 \\ 1 & 2 \end{pmatrix} \begin{pmatrix} 4 & 3 \\ 1 & 2 \end{pmatrix}$
Perform the matrix multiplication.
Multiply rows of the first matrix by columns of the second matrix.
For the element in the first row, first column: $(4 \times 4) + (3 \times 1) = 16 + 3 = 19$
For the element in the first row, second column: $(4 \times 3) + (3 \times 2) = 12 + 6 = 18$
For the element in the second row, first column: $(1 \times 4) + (2 \times 1) = 4 + 2 = 6$
For the element in the second row, second column: $(1 \times 3) + (2 \times 2) = 3 + 4 = 7$
Form the resulting matrix $P^2$ .
$P^2 = \begin{pmatrix} 19 & 18 \\ 6 & 7 \end{pmatrix}$
The calculated value of $P^2$ is $\boxed{\begin{pmatrix} 19 & 18 \\ 6 & 7 \end{pmatrix}}$ .

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