Question 305444
[A]={{{(matrix(2,2,1,-1,-2,3))}}}
[x]={{{(matrix(2,1,x1,x2))}}}
[b]={{{(matrix(2,1,3k,k-2))}}}
[A][x]=[b]
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[A]inv={{{(matrix(2,2,3,1,2,1))}}}
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[x]=[A]inv[b]={{{(matrix(2,2,3,1,2,1))*(matrix(2,1,3k,k-2))=(matrix(2,1,9k+k-2,6k+k-2))}}}
[x]={{{(matrix(2,1,10k-2,7k-2))}}}
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The system is consistent for all values of k.