-2 3 1. Let A 5 14 3 32 = such that B A into B)...

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-2 3 1. Let A 5 14 3 32 = such that B A into B) 2. Let A = = and B = ( 3 3 2 1-2 3 Find three elementary matrices E1, E2, and E -5 -1 E3E2E1A. (Hint: notice that three elementary row operations are used to transform ( 2 ). 1 (a) Show that the Reduced Row Echelon Form of A is the identity matrix I2. (b) Find every elementary matrix corresponding to each of the elementary row operation used in (a). (c) Use the result in (a) and (b) to write the inverse of A as a product of elementary matrices. 3. Use the Gauss-Jordan method to find the inverse of A 05 -2 4 12-10 -3 4-1 5 5 " if it exists. 1 0 4. Let A 3 1 2 2 -3 2 (a) Use the Gauss-Jordan method to find A-. (b) Use the result in (a) to solve the linear system (c) Find the inverse of the linear map T(x, y, z) = (x x- z = 0 -3x+y+2z = -3 2x - - 3y+2z = 1 z, -3x+y+2z, 2x 3y+2z). 5. Let T(x, y, z) = (x y + 2z, y 3z) and G(a, b) = (3a + b, a b, a 2b) - (a) Find (TG)(a, b). - (b) Find (GT)(x, y, z). -2 3 1. Let A 5 14 3 32 = such that B A into B) 2. Let A = = and B = ( 3 3 2 1-2 3 Find three elementary matrices E1, E2, and E -5 -1 E3E2E1A. (Hint: notice that three elementary row operations are used to transform ( 2 ). 1 (a) Show that the Reduced Row Echelon Form of A is the identity matrix I2. (b) Find every elementary matrix corresponding to each of the elementary row operation used in (a). (c) Use the result in (a) and (b) to write the inverse of A as a product of elementary matrices. 3. Use the Gauss-Jordan method to find the inverse of A 05 -2 4 12-10 -3 4-1 5 5 " if it exists. 1 0 4. Let A 3 1 2 2 -3 2 (a) Use the Gauss-Jordan method to find A-. (b) Use the result in (a) to solve the linear system (c) Find the inverse of the linear map T(x, y, z) = (x x- z = 0 -3x+y+2z = -3 2x - - 3y+2z = 1 z, -3x+y+2z, 2x 3y+2z). 5. Let T(x, y, z) = (x y + 2z, y 3z) and G(a, b) = (3a + b, a b, a 2b) - (a) Find (TG)(a, b). - (b) Find (GT)(x, y, z).