For a system of n non homogeneous equations in n variables equations let A, B and X represent the coefficient, constant and variable matrices. Then,

If $| A | \neq$ 0, then X = $A^{- 1}$ B gives a trivial solution.

True

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False

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Solution

The correct option is B
False

When $| A | \neq$ , the X = $A^{- 1}$ B gives a solution and is consistent but the solution will be a non trivial one because the given equations are non homogeneous and won’t satisfy (0,0,0) as solution. So the statement is false.

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Similar questions

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Q. Assertion :If a, b, c

ϵ R

and

a \neq b \neq c

and x, y, z are non zero. Then the system of equations

a x + b y + c z = 0

b x + c y + a z = 0

c x + a y + b z = 0

has infinite solutions. Reason: If the homogeneous system of equations has non trivial solution, then it has infinitely many solutions.

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For a system of n non homogeneous equations in n variables equations let A, B and X represent the coefficient, constant and variable matrices. Then, If |A|≠ 0, then X = A−1 B gives a trivial solution.

The correct option is B False When |A|≠, the X = A−1B gives a solution and is consistent but the solution will be a non trivial one because the given equations are non homogeneous and won’t satisfy (0,0,0) as solution. So the statement is false.

For a system of n non homogeneous equations in n variables equations let A, B and X represent the coefficient, constant and variable matrices. Then,

If $| A | \neq$ 0, then X = $A^{- 1}$ B gives a trivial solution.

The correct option is B
False

When $| A | \neq$ , the X = $A^{- 1}$ B gives a solution and is consistent but the solution will be a non trivial one because the given equations are non homogeneous and won’t satisfy (0,0,0) as solution. So the statement is false.