Equal Matrices (Sample Questions)


Example 1:
State the values of the unknowns in the following pairs of equal matrix.
( 1 x + 2 4 y 1 ) = ( 1 3 2 1 )

Solution:

( 1 x + 2 4 y 1 ) = ( 1 3 2 1 )

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.
(a) ( 3 2 p + q p 3 ) = ( 3 1 8 2 q 3 ) (b) ( 10 0 5 p 8 1 ) = ( p 2 q 0 4 q 1 )

Solution:
(a) ( 3 2 p + q p 3 ) = ( 3 1 8 2 q 3 )

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) ( 10 0 5 p 8 1 ) = ( p 2 q 0 4 q 1 )

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

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