practice book gate

Question

The number of linearly independent solutions of the system of equations

is equal to

A- 1

B- 2

C-3

D- 0

Answer 1

so option (d) is correct

Comments

Its should have infinite solutions Right?

is there any mistake in the question?

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no question is coorect

if we solve this matrix then rank =2

and here it ios asking for number of LI solutions = n.o of variables- rank

thats why answer is 1

hope u got it

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first of all given equation is not Linearly independent.if we assume a question printing mistake then it's Linearly dependent, in this case solution of equation is 1.

Because nullity(A) = rank(A) – no. of columns of A