Let T(x, y, z)=(-4r + 2z, 2x-3y-22, x+2y-2) be a transformation. (a) How would you determine...

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Let T(x, y, z)=(-4r + 2z, 2x-3y-22, x+2y-2) be a transformation. (a) How would you determine whether or not T is a linear transformation? (Explain in words. Be as detailed as possible.) (b) Assuming T is a linear transformation, is T one-to-one? Why or why not? . 1 2 Find two nontrivial" 4 x 3 matrices A and B such that A - B = 0 must show that A-B= 1 1 1 2 2 2 0 0 0 -2-2-2) -) 1 2 0 -2-2-2, 2 0 (You Find two nontrivial* 4 x 4 matrices A and B such that AB BA. (You must show that AB=BA.) Find a 2 x 2 matrix A such that the determinant of A is 7. (You must show that det(A) = 7.) . True or False: If A is an m x m matrix and has m pivot columns, then the columns of A form a linearly dependent set. (You must justify your answer.) *Nontrivial means you cannot use the zero matrix or the identity matrix. Let T(x, y, z)=(-4r + 2z, 2x-3y-22, x+2y-2) be a transformation. (a) How would you determine whether or not T is a linear transformation? (Explain in words. Be as detailed as possible.) (b) Assuming T is a linear transformation, is T one-to-one? Why or why not? . 1 2 Find two nontrivial" 4 x 3 matrices A and B such that A - B = 0 must show that A-B= 1 1 1 2 2 2 0 0 0 -2-2-2) -) 1 2 0 -2-2-2, 2 0 (You Find two nontrivial* 4 x 4 matrices A and B such that AB BA. (You must show that AB=BA.) Find a 2 x 2 matrix A such that the determinant of A is 7. (You must show that det(A) = 7.) . True or False: If A is an m x m matrix and has m pivot columns, then the columns of A form a linearly dependent set. (You must justify your answer.) *Nontrivial means you cannot use the zero matrix or the identity matrix.