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Determinants (Question no 1 a and b complete solution)
Determinants – Question No 1 (a & b) – Complete Solutions Introduction: Determinants are a fundamental part of linear algebra. They are used to solve systems of equations, find inverses of matrices, and analyze transformations. In this post, we will solve Question No 1 (a & b) step by step, with clear explanations, so students can understand and apply these methods to similar problems. Question 1 (a) Problem: Find the determinant of the following 2×2 matrix: A = | 2 3 | | 5 7 | Step-by-Step Solution: Formula for 2×2 matrix determinant: det(A) = ad - bc Substitute values: a=2, b=3, c=5, d=7 → det(A) = (2*7) - (3*5) Calculate: det(A) = 14 - 15 = -1 Answer: det(A) = -1 Tip: Always multiply diagonals carefully and check the sign. Question 1 (b) Problem: Find the determinant of the following 3×3 matrix: B = | 1 2 3 | | 0 4 5 | | 1 0 6 | Step-by-Step Solution: Choose method: We will use cofactor expansion along the first row....
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