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Math 300 Sec1.6 - Sec 2.1 Due date: Name ...... ID#. Sec#. Sec. 1.6 Q1: Solve the system by inverting the coefficient matrix ( X = A-'b) 1- 2- 5x + 6x2 = 9 2x + 2x2 + x3 = -1 2x + 3x2 + x3 = 3 Q2) Determine conditions on the bi's, if any, in order to guarantee that the linear system is consistent 1- 6x1 - 4x2 = b 3x - 2x2 = 2 2- X1 - 2x2 + 5x3 = b 4x1 - 5x2 + 8x3 = b - 3x + 3x - 3x) = b; 7 Q3) Solve the matrix equation for X 1 - 1 5 2 3 0 X = 4 0 -3 5-7 0 1 0 2 -1 3 2 1 Sec. 1.7 Q4) a) Find A1, A2, A and Ak 1- 2- 0 A= [: A= -6 0 0 0 30 0 0 5 -2 b) Compute 1- 2- [: -:] [: - Exercise Set 2.1 Q5: Find all the minors and cofactors of the matrix A 1 - 2 3 A= 6 7 1 4 Q6) Use the arrow technique to evaluate the determinant. 1- 2- - 1 3 1 1 2 0-51 7 2 -2 3 1 5 -7 6 2 Q7) Evaluate the determinant in Q6 part 1, by a cofactor expansion along (a) the first row. (b) the first column. (c) the second row. (d) the second column. (e) the third row. (f) the third column. Q8) Evaluate the determinant. 3. To 0 0 0 0 0 1 2 0 0 0 3 0 2 04 30 1 2 3 8 100 200 -23 0 0 0 A= 0 0 1 40 0 0 5 10 0 3