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Addition/ subtraction of matrices
Last updated at June 7, 2023 by Teachoo
Ex 3.2, 22 (Introduction) Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 , and p × k respectively. If n = p, then the order of the matrix 7X – 5Z is (A)p × 2 (B) 2 × n (C) n × 3 (D) p × n X =[■8(1&0@2&3)]_(2 × 2) 7X =[■8(7&0@14&21)]_(2 × 2) 7X – 5Z =[■8(𝟕&𝟎@𝟏𝟒&𝟐𝟏)]_(𝟐 × 𝟐)– [■8(𝟎&𝟏𝟎@𝟏𝟓&𝟓)]_(𝟐 × 𝟐)=[■8(𝟕&−𝟏𝟎@−𝟏&𝟏𝟔)]_(𝟐 × 𝟐) Therefore, ∴ Order of X = Order of 7X & Order of Z = Order of 5Z And, Order of 7X – 5Z = Order of 7X = Order of 5Z Ex 3.2, 22 Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 , and p × k respectively. If n = p, then the order of the matrix 7X – 5Z is (A)p × 2 (B) 2 × n (C) n × 3 (D) p × n Order of matrix X = 2 × n Order of matrix 7X = 2 × n Order of matrix Z = 2 × p Order of matrix 5Z = 2 × p ∴ Order of matrix 5Z = 2 × n ∴ Order of 7X – 5Z = Order of 7X = Order of 5Z = 2 × n. Hence, Correct answer is B