NO CREDIT WILL BE GIVEN FOR USING METHODS OUTSIDE OF CHAPTER 1. 7. Verify (B - C)A = BA - CA. (10 points) 1. The following represents the reduced row echelon form of an augmented matrix obtained from a linear system. Write the solution to the system. (5 points) 1000 0 2 8. Solve the following by finding A-1. No credit will be given for any other method. (10 points) 0 0 01 0 0 0 0 0 1 0 4x - 7y = 30 2. Determine any values of h and k such that the system of linear equations is inconsistent. (10 points) 6x - 9y = -39 2x + 5y = -1 hx + 5y = k 9. Give an example of each of the following, if it exists. If it doesn't exist, briefly explain why. 3. Consider the following matrices and their sizes: (10 points) A 2X4 B 2X4 C 5X2 D 4X2 E 5X4 a. A 4x3 lower triangular matrix. Determine which of the following quantities are defined. If the quantity is defined, give the size of the b. A 4x4 symmetric matrix resulting matrix or state if the quantity is a scalar. If the quantity is undefined, briefly explain why. c. An invertible diagonal matrix (2 points each) a. BAT + D b. tr (AD)ET c. D-1 d. tr(CTEB) e. (A - B)D 10. Assume all matrices are sizes such that the multiplication is defined. Solve for X. (10 points) 4. Consider the following matrix: (BAT)TX(BCT)-1 = A A = 2 2 -2) Find A-1, if it exists or briefly explain why it doesn't. (10 points) 11. If possible, find the following. If not, briefly explain why. (5 points each). 5. If A = ( _2) and p(x) = x3 -3x - 4, find p(A). (10 points) -5 2 a. A-2 if A = 0 0 7 6. Let T be a linear transformation from R3 to Ragiven by x+1 b. The values of x such that the following matrix is invertible 3 x2-3x-4 T(x1, X2, X3) = (3x1 - 5x2 + X3,X1 + 6X3) 3 x2 - Find the standard matrix of the transformation. (5 points)