standard basis of R4. We have (0, 0, -3,0), Let : R4 R4 be a linear...

 

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standard basis of R4. We have (0, 0, -3,0), Let : R4 R4 be a linear map and let B = (e1) = (-6,6,0,0), (2) = {e1, e2, e3, e4} be the (-3,3,0,0), = (e4) = (6, -6, -3,0). 1. Find the matrix corresponding to with respect to the standard basis B. (e3) 2. Let ae1e2, b = e1-e2 - e3, c = 2e12e2e3 + e4,d = e1 + 2e2. Show that B' = {a, b, c, d} is a basis of R4. 3. Compute (a), (b), (c), (d). 4. Find the matrix corresponding to with respect to the basis B'. 5. Find ker() and Im(). Find the dim(ker()) and dim(Im()). standard basis of R4. We have (0, 0, -3,0), Let : R4 R4 be a linear map and let B = (e1) = (-6,6,0,0), (2) = {e1, e2, e3, e4} be the (-3,3,0,0), = (e4) = (6, -6, -3,0). 1. Find the matrix corresponding to with respect to the standard basis B. (e3) 2. Let ae1e2, b = e1-e2 - e3, c = 2e12e2e3 + e4,d = e1 + 2e2. Show that B' = {a, b, c, d} is a basis of R4. 3. Compute (a), (b), (c), (d). 4. Find the matrix corresponding to with respect to the basis B'. 5. Find ker() and Im(). Find the dim(ker()) and dim(Im()).

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