ECON 1540 Study Guide - Midterm Guide: Determinant, Invertible Matrix, Conjugate Transpose

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Question 1: (a) determine the rank of matrix b below (8 marks) B = 2 3 -5 0 1 5 9. 3 3 6 -15 9 r(b) = 3 r(b) = 4 (b) how many linearly independent columns are inside b? (3) If the answer to part (d) is no, which equation gets in the way of solving the system? (3 marks) n - r(a) = 2 0 2 (a) find the determinant of a using a co-factor expansion. (do not use saurus rule. ) 1 x2 = |d2| / |a| = -7. 000, where d2 = x3 = |d3| / |a| = -0. 750, where d3 = Answer the following using the same matrix a as in question 3. (a is written again below) (a) find the adjoint matrix of a and the inverse of matrix of a (14 marks) 2 10 (b) solve the system a x = 3 2 using the inverse matrix in part (a).

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