If (21, 22, 23) R, let: 1 1 =det 12 13 2 3 4 5...

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If (21, 22, 23) € R³, let: 1 1 =det 12 13 2 3 4 5 6 T(1,2,3)= (1.16) (a) Expand the determinant to find a formula for T(1, 22, 23). (b) Show that equation (1.16) defines a linear transformation T: R³ R. (c) Find the matrix of T with respect to the standard bases. (d) The matrix you found in part (c) should be a 1 by 3 matrix. Thinking of it as a vector in R³, show that it is orthogonal to both (1,2,3) and (4,5,6), the second and third rows of the matrix used to define T(21, 22, 23).. If (21, 22, 23) € R³, let: 1 1 =det 12 13 2 3 4 5 6 T(1,2,3)= (1.16) (a) Expand the determinant to find a formula for T(1, 22, 23). (b) Show that equation (1.16) defines a linear transformation T: R³ R. (c) Find the matrix of T with respect to the standard bases. (d) The matrix you found in part (c) should be a 1 by 3 matrix. Thinking of it as a vector in R³, show that it is orthogonal to both (1,2,3) and (4,5,6), the second and third rows of the matrix used to define T(21, 22, 23)..

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a To expand the determinant we can use the properties of determinants Lets expand the determinant T2... View the full answer