Midterm Fall 2007 Shotz

# When a given one column matrix b is appended to a to

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When a given one column matrix, B, is appended to A to make an augmented matrix A aug = (A | B), we find that rank (A aug ) = 5. Then a) The equation AX = B has no sol’n and the equation AX = 0 has only one sol’n. b) The equation AX = B has many sol’ns and so does AX = 0. c) The equation AX = B has no sol’n, but the equation AX = 0 has many sol’ns. d) Not enough information is given to determine existence and number of solutions for AX = B and AX = 0. e) None of these. ----------------------------------------------------------------------------------------------

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-------------------------------------------------------- page 3 (Your name) III) We seek a 5 x 5 real matrix, A, that satisfies A 4 = -c I, where I is the 5 x 5 identity matrix and c is a given real number. a) If c ≥ 0, the only solutions are singular matrices and there may be no solution for certain values of c. b) There are numbers c < 0 for which no solution exists. c) A real matrix, A, can be found as a solution for any c ≠ 0. d) No matter what value of c we choose, a solution matrix, A, is non-singular. e) None of these. ------------------------------------------------------------------------------------------------------ IV) A certain 4 x 4 matrix, A, is given; we append to it a 4 x 4 identity matrix to form

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