GATE EE 2024 Set 1 — Question 11
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Engineering Mathematics → Linear Algebra → Determinants
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Question
Which one of the following matrices has an inverse?
Correct answer
(C) bmatrix 1 & 4 & 8 \ 0 & 4 & 2 \ 1 & 2 & 4 bmatrix
Solution
A matrix has an inverse if and only if its determinant is non-zero.
(A) In this matrix, . Since rows are linearly dependent, the determinant is .
(B) In this matrix, . Since rows are linearly dependent, the determinant is .
(D) In this matrix, . Since rows are linearly dependent, the determinant is .
(C) Let's calculate the determinant of matrix C:Since , matrix (C) has an inverse.
(A) In this matrix, . Since rows are linearly dependent, the determinant is .
(B) In this matrix, . Since rows are linearly dependent, the determinant is .
(D) In this matrix, . Since rows are linearly dependent, the determinant is .
(C) Let's calculate the determinant of matrix C:Since , matrix (C) has an inverse.
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