PROBLEMS ON EQUALITY OF MATRICES

Problem 1 :

Find the values of p, q, r, and s, if

Solution :

Since the given two matrices are equal, the corresponding elements must be equal.

Then, we have

Solve (1) for p.

p² - 1 = 1

p² = 2

p = ±√2

Solve (2) for q.

-31 - q³ = -4

-q³ = 27

q³ = -27

q = -3

Solve (3) for q.

r + 1 = ³⁄₂

r = ½

Solve (4) for r.

s - 1  =  -π 

s  = -π + 1

Problem 2 :

Determine the value of x + y, if

Solution :

2x + y = 7 ----(1)

4x = x + 6 ----(2)

Solve (2) for x.

4x = x + 6

3x = 6

x = 2

Substitute x = 2 into (1).

2(2) + y = 7

4 + y = 7

y = 3

The value of (x + y) :

x + y = 2 + 3

x + y = 5

Problem 3 :

Determine the matrices A and B, if they satisfy

Solution :

(1) - 2(2) :

Substitute the matrix B found above into (2).

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