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For the linear system x1+3x2=2 3x1+hx2=k Find values for h and k such that the system...

For the linear system x₁+3x₂=2 3x₁+hx₂=k

Find values for h and k such that the system has:

a) no solution

b) a unique solution

c) infinitely many solutions

Solutions

Expert Solution

Solution:

If , the rank of is and the rank of is .

The system will be inconsistent and will have no solution.

The system has a unique solution if the coefficient matrix is non-singular

If , the coefficient matrix and the augmented matrix become

The rank of is and the rank of will also be if

If and , the system is consistent . But the rank of is less than the number of unknown . Hence , will have infinite solutions.

milcah answered 1 year ago

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