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Mathematics · Class 10 · Chapter 19: Matrices and Determinants

8 min

Key points

Matrix is a rectangular array of numbers arranged in rows and columns
Order of matrix is written as m × n where m = number of rows, n = number of columns
Square matrix has equal number of rows and columns (n × n)
Determinant can only be calculated for square matrices
For 2×2 matrix, determinant = ad - bc where matrix elements are [[a,b],[c,d]]
For 3×3 matrix, use expansion by cofactors method
Addition and subtraction of matrices is only possible when they have same order
Matrix multiplication A×B is possible only when number of columns in A = number of rows in B
Identity matrix has 1's on main diagonal and 0's elsewhere
Inverse of matrix A exists only when det(A) ≠ 0

Definitions

Matrix: A matrix is a rectangular array of numbers arranged in rows and columns enclosed within square brackets or round brackets.
Order of Matrix: The order of a matrix is the number of rows and columns it contains, written as m × n where m is the number of rows and n is the number of columns.
Square Matrix: A matrix in which the number of rows is equal to the number of columns is called a square matrix.
Determinant: The determinant of a square matrix is a number associated with the matrix which is calculated by a specific method.
Identity Matrix: An identity matrix is a square matrix in which all the diagonal elements are 1 and all other elements are 0.

Worked example

Define matrix and find the determinant of matrix A = [[2, 3], [1, 4]]. Also verify that det(A) ≠ 0. (6 marks)

Matrix: A rectangular arrangement of numbers in rows and columns enclosed by brackets. For matrix A = [[2, 3], [1, 4]], det(A) = (2)(4) - (3)(1) = 8 - 3 = 5. Since det(A) = 5 ≠ 0, verification is complete.

Common mistakes

Students confuse rows and columns when writing matrix order
Forgetting the formula det = ad - bc for 2×2 matrices
Attempting to add matrices of different orders
Mixing up matrix multiplication with element-wise multiplication
Not checking if matrix multiplication is possible before solving

Quick recap

Matrix is a rectangular arrangement of numbers in rows and columns. Order is written as m×n (rows × columns). For 2×2 matrix, determinant = ad - bc. For 3×3 matrices, use cofactor expansion. Matrix operations include addition, subtraction, and scalar multiplication following specific rules.

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