Question

Which of the following is a diagonal matrix.

(a) A=\(\begin{bmatrix}0&2&1\\2&0&1\\2&1&0\end{bmatrix}\)

(b) A=\(\begin{bmatrix}5&1&0\\0&5&0\\0&0&5\end{bmatrix}\)

(c) A=\(\begin{bmatrix}4&0&0\\0&5&0\\0&0&9\end{bmatrix}\)

(d) A=\(\begin{bmatrix}2&2&2\\3&3&3\\4&4&4\end{bmatrix}\)

I got this question in an interview for internship.

I'm obligated to ask this question of Types of Matrices in section Matrices of Mathematics – Class 12

Answer 1

Correct choice is (c) A=\(\begin{bmatrix}4&0&0\\0&5&0\\0&0&9\end{bmatrix}\)

Explanation: The matrix is said to be a diagonal matrix if the elements along the diagonal of the matrix are non – zero.

i.e. aij=0 for i≠j and  aij≠0 for i=j.

Therefore, the matrix A=\(\begin{bmatrix}4&0&0\\0&5&0\\0&0&9\end{bmatrix}\) is a diagonal matrix.