1. [-/10 Points] DETAILS LARLINALGB 2.3.075. Under what conditions will the diagonal matrix #11 0 0 0 be invertible? Assume A is invertible and find its inverse. Use your result to find A" for each matrix. 70 050 0 0 -4 A1 = (b) A= Need Help? Read It2. [-/10 Points] DETAILS LARLINALG8 2.1.047. Write the system of linear equations in the form Ax = b and solve this matrix equation for *. 1 3 -9 *1 Need Help? Read It 3. [-/5 Points] DETAILS LARLINALG8 2.2.071. Determine whether the matrix is symmetric, skew-symmetric, or neither. A square matrix is called skew-symmetric when A = -4. A =23 O symmetric O skew-symmetric O neither Need Help? Read It4. [-/5 Points] DETAILS LARLINALG8 2.2.076. Prove that if A and 8 are n x n skew-symmetric matrices, then A + 8 is skew-symmetric. By the definition of skew-symmetric, if A and 8 are n * n skew-symmetric matrices, we get which of the following? O AT = A and BY = B O Al = 1 and B-1 = 1 O Al = A and 8-1 = B O AT = -A and BT = -B OAl = -A and 8-1 = -B O AT = 1 and BY = 1 Using these definitions we then get which of the following? O (A + B) ] = Al + Bl = 1 + 1 = 21 O (A + B)7 = AT + BT = A + B O (A + B ) = AT + BT = -A - B = -(A + B) O ( A + B) 1 = Al + 8-1 = -A - B = -(A + B) O ( A + B ) 1 = Al + 8 1 = A + B O (A + B) = AT + B) = 1 + 1 = 21 This proves that A + 8 is skew-symmetric. Need Help? Read It 5. [-/10 Points] DETAILS LARLINALG8 2.3.051. Use a software program or a graphing utility with matrix capabilities to solve the system of linear equations using an inverse matrix. 2x1 - 3, + X - 2X4 XE - 4X- = 16 - X5 + 286 = 0 + x 2 4X1 7 + 4x4 X5 + 2X6 = -2 -5X1 - - X27 + 4x, + 2x4 - - 5X5 + 3X6 = -22 *1 + X 2 + 4 XA - - 3X 3 + 4) 3X5 + X6 = -9 2X3 - 3x4 + 2X5 - OX6 = 28