2.2.1 Equal Matrices (Sample Questions)

Example 1:

State the values of the unknowns in the following pairs of equal matrix.

(\begin{matrix} 1 & x + 2 \\ 4 - y & - 1 \end{matrix}) = (\begin{matrix} 1 & 3 \\ 2 & - 1 \end{matrix})

Solution:

(\begin{matrix} 1 & x + 2 \\ 4 - y & - 1 \end{matrix}) = (\begin{matrix} 1 & 3 \\ 2 & - 1 \end{matrix})

x + 2 = 3
x = 1

4 – y = 2
–y = –2
y = 2

Example 2:

Calculate the values of p and q in each of the following matrix equations.

\begin{array}{l} (a) (\begin{matrix} 3 & 2 p + q \\ p & - 3 \end{matrix}) = (\begin{matrix} 3 & 1 \\ 8 - 2 q & - 3 \end{matrix}) \\ (b) (\begin{matrix} 10 & 0 \\ 5 p - 8 & 1 \end{matrix}) = (\begin{matrix} p - 2 q & 0 \\ - 4 q & 1 \end{matrix}) \end{array}

Solution:

(a) (\begin{matrix} 3 & 2 p + q \\ p & - 3 \end{matrix}) = (\begin{matrix} 3 & 1 \\ 8 - 2 q & - 3 \end{matrix})

2p + q = 1

q = 1 – 2p —-(1)

p = 8 – 2q —-(2)

Substitute (1) into (2),

p = 8 – 2(1 – 2p)

p = 8 – 2 + 4p

p – 4p = 6

–3p = 6

p = –2

Substitute p = –2 into (1),

q = 1 – 2(–2)

q = 5

(b) (\begin{matrix} 10 & 0 \\ 5 p - 8 & 1 \end{matrix}) = (\begin{matrix} p - 2 q & 0 \\ - 4 q & 1 \end{matrix})

10 = p – 2q

p = 10 + 2q —-(1)

5p – 8 = –4q —-(2)

Substitute (1) into (2),

5 (10 + 2q) – 8 = –4q

50 + 10q – 8 = –4q

14q = –42

q = –3

Substitute q = –3 into (1),

p = 10 + 2(–3)

p = 4