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 isabcdis given by:

D2×2 = ad - bc

The 3 by 3 matrix determinant formula is [abcdefghi] is given by:

D3×3 = 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: [2348]

  • Sol:
  • To find the Determinant of the matrix.
  • Given: a = 2; b = 3; c = 4; d = 8
  • Using the determinant formula,
  • D2×2 = ad - bc
  • Put the values,
  • D2×2 = 2(8)-3(4)
  • = 16-12
  • = 4
  • Answer: Determinant of the matrix is 4.

Example 2: Find the determinant of the 3x3 matrix below: [6114-25287]

  • 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,
  • D3×33×3 =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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Determinant Formula
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