Let S be the set of 2 2 upper triangular matrices and define B = }]}...

    

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Let S be the set of 2 2 upper triangular matrices and define B = }]} and C = c = {(63-6 1-6 9} (a) Show that S is a subspace of R22. [4 points] (b) It is known that C is a basis for S. Find the coordinate vector [X]c, where x = [13]. [2 points] 03 (c) Show that B is a basis for S. [4 points] (Hint: Consider the coordinate vectors of B relative to C.) (d) Find the change-of-coordinates matrix from C to B, PB+C. [4 points] (e) Find the coordinate vector [X]B. [3 points] Let S be the set of 2 2 upper triangular matrices and define B = }]} and C = c = {(63-6 1-6 9} (a) Show that S is a subspace of R22. [4 points] (b) It is known that C is a basis for S. Find the coordinate vector [X]c, where x = [13]. [2 points] 03 (c) Show that B is a basis for S. [4 points] (Hint: Consider the coordinate vectors of B relative to C.) (d) Find the change-of-coordinates matrix from C to B, PB+C. [4 points] (e) Find the coordinate vector [X]B. [3 points]