For a system of n linear equations in n variables, let A, B and X represent the coefficient, constant and variable matrices.If $| A | = 0$ , and (adj A). B $\neq$ 0 the system of equations is inconsistent and has no solution.

True

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False

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Solution

The correct option is A
True

This is a important result to remember because when then system of equations can either have no or infinite number of solutions. The condition with which we can test this is if (adj. A).B $\neq$ 0 then no solution i.e., inconsistent and if (adj.A).B=0 then infinite solution i.e., consistent.

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For a system of n linear equations in n variables, let A, B and X represent the coefficient, constant and variable matrices.If |A|=0, and (adj A). B ≠ 0 the system of equations is inconsistent and has no solution.

For a system of n linear equations in n variables, let A, B and X represent the coefficient, constant and variable matrices.If $| A | = 0$ , and (adj A). B $\neq$ 0 the system of equations is inconsistent and has no solution.