JEE Main 2025 Syllabus PDF - Subject-Wise Detailed Syllabus

# Singular Matrix - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• Determinant of a Matrix, Singular and Non-singular Matrix is considered one of the most asked concept.

• 45 Questions around this concept.

## Solve by difficulty

If

then k is equal to:

If a>0 and discriminant of is -ve, then  is

If are the cube roots of unity, then

Let a, b, c be such that  .If

then the value of is

## Concepts Covered - 2

Determinant of a Matrix, Singular and Non-singular Matrix

Determinant of a matrix A is a number which is calculated from the matrix. For determinant to exist, matrix A must be a square matrix. Determinant of matrix is denoted by det A or |A|.

For 2 x 2 matrices

$\\\mathrm{A = \begin{bmatrix} a_1 & a_2\\ b_1 & b_2 \end{bmatrix}} \\\\\mathrm{then\; det A\; is:} \\\\\mathrm{|A| = \begin{vmatrix} a_1 & a_2\\ b_1 & b_2 \end{vmatrix} = a_1\times b_2 - a_2\times b_1} \\\\\mathrm{For \;a \;3 \times 3\; matrix\; determinant\; can \;be\; calculated\; in\; the\; following\; way:} \\\\\mathrm{let\;A = \begin{bmatrix} a_1 & a_2 & a_3\\ b_1 & b_2 & b_3\\ c_1 & c_2 & c_3 \end{bmatrix} } \\\\\mathrm{then\; we \; find \ det \; A\; in \; following\; way} \\\\\mathrm{|A| = a_1(b_2\cdot c_3-b_3\cdot c_2) - a_2 (b_1\cdot c_3-c_1b_3) +a_3(b_1c_2-b_2c_1)}$

This same process we follow to evaluate the determinant of the matrix of any order. Notice that we start first term with +ve sign and then 2nd with -ve sign and 3rd again +ve sign, this sign sequence is followed for any order of matrix.

This whole process is row dependent, same process can be done using column, means we can select element along column and delete their row and column and compute the determinant of left out matrix and then multiply it with the element which we select. And we will get the same result as we get while doing the whole process along row.

Singular and non-singular matrix:

A square matrix is called singular matrix if its determinant is 0 otherwise it is called non-singular matrix. Let say A is a square matrix then it is singular if |A| = 0, otherwise, it will be non-singular if |A| ≠ 0.

Properties of Determinant of a Matrix

Properties of Determinants - Part 4

If A and B are square matrices of same order:

i) det (A’) =  det A

ii) det (AB) = det (A) det (B) and |AB| = |BA|

iii) if A is skew symmetric matrix of odd order then |A| = 0.

iv) if A is a skew symmetric matrix of even order then |A| is a perfect square.

v) |kA| = kn |A|, where n is order of A

vii) |An| = |A|n, where n ? N.

## Study it with Videos

Determinant of a Matrix, Singular and Non-singular Matrix
Properties of Determinant of a Matrix

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