The coefficient matrix is:
A=(2510) The variable matrix is:
X=(pq) The constant matrix is:
B=(58) Thus, to solve a system AX=B, for X, multiply both sides by the inverse of A
A−1AX=A−1B and we shall obtain the solution:
X=A−1BProvided the inverse A−1 exists, this formula will solve the system.
detA=∣A∣=∣∣2510∣∣=2(0)−1(5)=−5=0 The inverse A−1 exists.
A−1=−51(0−5−12)=(011/5−2/5)
X=A−1B=(011/5−2/5)(58)
=(0(5)+(1/5)(8)1(5)+(−2/5)(8))=(8/59/5)
(pq)=(8/59/5)
p=8/5,q=9/5
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