Determinant Formula

About Determinant Formula

The determinant formula is used to quickly get the determinant of a matrix. It's a mathematical object that only works with square matrices. A square matrix has the same number of rows and columns as the number of columns.

What Is Determinant Formula?

A matrix's determinant is a number that only applies to square matrices. It is utilised in the study and solution of linear equations. The determinant formula is used to derive the determinant of a matrix from its constituents.

Determinant Formula:

The 2 by 2 matrix determinant formula that is$\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ \mathrm{c}& \mathrm{d}\end{array}\right]$is given by:

D_2×2 = ad - bc

The 3 by 3 matrix determinant formula is [$\left[\begin{array}{ccc}\mathrm{a}& \mathrm{b}& \mathrm{c}\\ \mathrm{d}& \mathrm{e}& \mathrm{f}\\ \mathrm{g}& \mathrm{h}& \mathrm{i}\end{array}\right]$] is given by:

D_3×3 = a(ei-fh)-b(di-fg)+c(dh-eg)

Applications of Determinant Formula

Determinants are mathematical objects that can be used to solve and analyse systems of linear equations. Determinants are used in a variety of fields including engineering, science, economics, and social science. More Maths Formulas on the parent's page.

Solved Example of Determinant Formula

Example: Find the determinant of the 2x2 matrix below: [$\left[\begin{array}{cc}\mathrm{2}& \mathrm{3}\\ \mathrm{4}& \mathrm{8}\end{array}\right]$]

• Sol:
• To find the Determinant of the matrix.
• Given: a = 2; b = 3; c = 4; d = 8
• Using the determinant formula,
• D_2×2 = ad - bc
• Put the values,
• D_2×2 = 2(8)-3(4)
• = 16-12
• = 4
• Answer: Determinant of the matrix is 4.

Example 2: Find the determinant of the 3x3 matrix below: [$\left[\begin{array}{ccc}6& 1& 1\\ 4& -2& 5\\ 2& 8& 7\end{array}\right]$]

• Sol: To find the Determinant of the matrix
• a = 6; b = 1; c = 1
• d = 4; e = -2; f = 5
• g = 2; h = 8; i = 7
• Using the determinant formula,
• D_3×33×3 =a(ei - fh) - b(di - fg) + c(dh - eg)
• = 6(−2×7 − 5×8) − 1(4×7 − 5×2) + 1(4×8 − (−2×2))
• = 6(−54) − 1(18) + 1(36)
• = -306
• Answer: The determinant of the matrix is (-306).

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