Let L : R^3 → R^3 be the linear transformation mapping defined by L(x) = (2x1 − x2 − x3, 2x2 − x1 − x3, 2x3 − x1 − x2)^T. Determine the standard matrix representation A of L.

Find the global transformation matrix to transfer the local coordinate system (x1, y1, z1) to the global coordinate system (X0, Yo, Zo).

Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x₁, x₂, are not vectors but are entries in vectors T(X1X2 X3)(x₁ -5x + 6xy, X₂-7x3) A-(Type an integer or decimal for each matrix element.)

Find the standard matrix representation for each linear operator L : R^2 → R^2 described below:(a) L rotates each vector x by 45◦ in the clockwise direction. (b) L reflects each vector x about the x1 axis and then rotates it 90◦ in the counterclockwise direction. (c) L doubles the length of x and then rotates it 30◦ in the counterclockwise direction. (d) L reflects each vector x about the line x2 = x1 and projects it onto the x1 axis.

Consider a linear transformation T from R2 to R² for which (:) -}- T and T Find the matrix A of T. A =

Assume that T is a linear transformation. T: Projects vectors in its domain onto the line y = 2/3 x. Find the standard matrix of T. Enter your matrix as 4-tuple (a11, 12, 921, 922) Use only fractions in simplest form and integers. NO DECIMALS "a11 11 "),a12= ,a21= ,a22=

Find a formula for the linear transformation whose matrix representation given by

Let A be the 3 x 3 2D transformation matrix for refeletion about the r-axis. Show A.

Assume that T is a linear transformation. T: Projects vectors in its domain onto the line y = 4x. Find the standard matrix of T. Enter your matrix as 4-tuple (a11, 12, 021, 922) Use only fractions in simplest form and integers. NO DECIMALS "a11 11 "),a12= ,a21= ,a22=

Suppose T : R^2 → R^2 is a linear transformation that does not alter e_i andwhich maps e_2 into e_2 + 2e_1, where e_i = (1,0), e_2 = (0,1). Find the transformation matrix T.Justify your answer.