Use properties of the linear transformation T(x, y) = (3x − 2y, x + y) to determine if the matrix for T is invertible or not.

Use matrix multiplication to find the contraction of (a,b) with factor k =1 / infinity, where infinity is greater than 1

Compute the standard matrix for the linear map T : R² → R² which (1) rotates i by 0 = T, (2) stretches the x-component by 3 and (3) reflects the result of (2) about the T - axis.

Find the standard matrix of the given linear transformation from R² to R². Reflection in the line y = x

Assume that T is a linear transformation. Find the standard matrix of T.

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

Consider the (x, y) vertices of an equilateral triangle in R² given by, (0,0), (1,0), (.5, √3/2) Perform the following actions in order using matrix transformations: (a) Reflect the triangle over the x-axis, (b) Compress the triangle along the y-axis by a factor of 2, (c) Rotate the triangle counterclockwise by π/6 radians about the origin, and (d) Shear the triangle along the x-axis by a factor of 0.5. Clearly show the matrix transformations used and compute the final set of vertices of the triangle.

Determine whether or not the following linear transformation is invertible, and justify your answer

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

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]