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
p2 - 1 = 1 ----(1) r + 1 = ³⁄₂ ----(3) |
-31 - q3 = -1 ----(2) s - 1 = -π ----(4) |
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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