Consider the matrices

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

P=\begin{bmatrix}1&2&0\\-1&1&3\end{bmatrix}

Q=\begin{bmatrix}2&1\\0&1\\1&-2\end{bmatrix}

and

R=\begin{bmatrix}3&-1\\2&0\end{bmatrix}

. (i) Find

QR

. (ii) Find

P(QR)

. (iii) Find

PQ

. (iv) Find

(PQ)R

. (v) Prove that

P(QR)=(PQ)R

for the given matrices.