Let T be the linear transformation defined by T(х, у) %3D (-9у, 4х + у, 5у— 8х, 2у - 7x). Find its associated matrix A. A =

Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot product (Ab) * (Ac) as a product of matrices.

Construct a 4×3 matrix A and vectors ~b and ~c in R4 so that ~b is in the range ofthe linear transformation with standard matrix A but ~c is not.

Find the Jacobian of the transformation = 3u + 7v, y = u² - - v.

Let's create a matrix that reflects around a line that is perpendicular to the vector n = [0.375, 0.927] in 2D, this line passes though the origin. Now that you have both rows, what is the image of the point (1, 2) under this transformation? Enter the x-coordinate, round it to 3 decimal places.

Consider the matrix A = a1 a12 a13 a14 24, show that the product L(x)=Ai is a linear transformation, where žER“.

Find the image of the point (x, y) under the matrix transformation that first reflects the point with respect to the x-axis, then rotates the resulting point about the origin through an angle of T/3, and then reflects the resulting point with respect to the line y = x.

Let = A = - = The cross product of two vectors in R³ is defined by a1 a2 az X b₁ b₂ b3 = 0 E] 7 Find the matrix A of the linear transformation from R³ to R³ given by T(x) = V × ã. [a₂b3-a3b₂ a3b₁a₁b3 [a₁b₂-a₂b₁]

Find the standard matrix for the linear transformation T(1, 9) — (2а — Зу, т — у, у — 4г) -3 1 -1 1 1 -4 2 1 -4 -3 -1 1 -3 -1 2 1 1 -3 -1 2.

Let S be a linear transformation from R³ to R² with associated matrix Let T be a linear transformation from R² to R² with associated matrix Determine the matrix C of the composition To S. C= 2 4-843 3]. A = B = 2 21.