M = Find the matrix M of the linear transformation T: R³ → R² given by 3 X1 (E)- = X3 T -9x1 - x2 + -8x₁ + (-4) X3

A linear transformation T : R2 → R2 first reflects pointsabout the y-axis, then rotates points counterclockwise by 45 degrees.(a) Find the standard matrix of T. (b) Find the preimage of (−1, 4).

(4) Let B be the matrix 1 1 B = 2 3 4 -1 -3 1 -6 -2 and let TB : R4 → R³ be the linear transformation TB(x) = Bx.

Find the matrix M of the linear transformation T: R³ → R² given by T X1 x2 x 3 7x₁x₂ + (-4) x3 -4x1 + (-8) x₂

Assume that T is a linear transformation. Find the standard matrix of T. T: R2→R*, T(e,) = (8, 1, 8, 1), and T(e2) = (-6, 9, 0, 0), where e, = (1,0) and e, = (0,1).

Diagonalize the quadratic form by finding an orthogonal matrix Q such that the change of variable x- Qy transforms the given form into one with no cross-product Enter your answer in the form (Q. f(y)) = ([[row 1], [row 2]]. (y)). where each row is a comma- C terms. Give Q and the new quadratic form, f(y). (Assume y separated list and f(y) is in terms of y (Q. (y)) - 6x₁² + 9x₂² Need Help? - 4x₁x2 Read it and Y₂)

A freelance artist is paid $3,520 for a contracted job. The money is invested in a savings account earning 3.05% annual interest compounded monthly. What is the total account balance after 6 months?

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Find the matrix A of T. A= Consider a linear transformation T from R³ to R² for which = E T = [8]. T = T * (E) - · *(8) - · *(6) - A -H). =

Find the B-matrix for the transformation xAx, where B={b₁,b₂}- -5 - 1 2 = *[*) * * C A = b₁ b₂ 5 The B-matrix of the given transformation is