e fact that matrices A and 8 are row-equivalent. 8 0 -17 -5 1 5 -2 -5 1 3 -7 -15 23 5 -77 7 -13 5 10 1 0 1 -2 0 0 0 0 1 - 0 0 1 -3 10 3 (a) Find the rank and nullity of A. rank

Let B and F be the following matrices.       [ -9  -7  -3  -3 ] B=  [ 7  10  8  -8 ]       [ 6   5  -3   6 ]        [ -1  4 10  -5 ] F= [ -2  -7  0  -10 ]      [ 9   0   7   -5 ] Find the indicated quantity. B + F ______   ______    _______   _______ ______   ______   _______   ________ ______  _______  _______  ________

3 Let matrix A = 1 –12 (a) Find elementary matrices E,.,E, such that E,.E, A = I. Write your answer as a product like b e f 3 -12 1 -3 (b) Write A as the product elementary matrices. Hint, solve E,E, A=1 for A first ("algebraically"). Write your answer as a product like ... b 3 1 -12 -3

2. Orthogonally diagonalize the matrices. 7 -4 4 1 5 (a) (b) |-4 5 1 4 9

9 Matrix exponential Determine the three matrices V, D and 1-1 such that -- (You do not have to multiply the three matrices.) A

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