Use the variables t, s, r, . for free variables. X1 + x2 + x3 x4 = 4: (10 points) (a) let a =(cid:20)3. A, b, and c are invertible square matrices of the same size. Let y = (abc) 1 and z = (ab)t . Fill out each blank with y if y matches, z if z matches, and x if neither match. C 1(ab) 1 = (c) find the inverse of the matrix x = . Show all steps: (10 points) an elementary problem. (a) a = . Write down the corresponding elementary matrices and describe the elementary row operation which was performed. In terms of e1, e2, and e3, nd a formula for p such that p a = r. p = Singular. (b) write the matrix b =(cid:20)1 2. 3 4(cid:21) and its inverse b 1 as a product of elementary matrices: (10 points) determinants! Then re-compute the determinant using some other technique.
