How to Find Determinants of a Matrix?

A Matrix is an array of numbers: (m×n) with (m) rows and (n) columns. The determinant of a matrix is a scalar value that is defined for square matrices.

Related Topics

• How to Multiply a Matrix by a Scalar
• How to Add and Subtract Matrices

A step-by-step guide to finding determinants of a matrix

• The determinant of a (2×2) matrix (A), (A=begin{bmatrix}a & b c & d end{bmatrix}) is defined as (|A|=ad-bc).
• The determinant of a (3×3) matrix (A), (A=begin{bmatrix}a & b & c d & e & f g & h & iend{bmatrix}) is defined as (|A|=a(ei-fh)-b(di-fg)+c(dh-eg))

Finding Determinants of a Matrix – Example 1:

Evaluate the determinant of matrix (A=begin{bmatrix}5 & -1 6 & 2 end{bmatrix})

Solution:

The determinant is: (|A|=5(2)-(-1)(6)=10-(-6)=10+6=16)

Finding Determinants of a Matrix – Example 2:

Evaluate the determinant of matrix: (A=begin{bmatrix}2 & 0 & 1 & -1 & 1 3 & 1 & -2end{bmatrix})

Pre-Calculus for Beginners 2026 The Ultimate Step by Step Guide to Acing Precalculus

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Solution:

The determinant is: (|A|=2((-1)(-2)-(1)(1))-0((-2)(0)-(1)(3)+1((0)(1)-(-1)(3))=5)

Exercises for Finding Determinants of a matrix

Evaluate the determinants of each matrix.

• (color{blue}{begin{bmatrix}3 & 5 & 9 end{bmatrix}})
• (color{blue}{begin{bmatrix}0 & 1 4 & 6 end{bmatrix}})
• (color{blue}{begin{bmatrix}1 & 5 & 4 & 9 & 11 & 0 & 6end{bmatrix}})
• (color{blue}{begin{bmatrix}6 & 0 & 51 & 4 & 23 & 7 & 4end{bmatrix}})

• (color{blue}{27})
• (color{blue}{-4})
• (color{blue}{23})
• (color{blue}{-13})