11 + 1 Problem 4.1. Define T: R2 R by T(x)=-2r for all x = [2x...

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11 + 1₂ Problem 4.1. Define T: R2 R³ by T(x)=₁-2r₂ for all x = [2x₁ -2] -D- (1) Find the standard matrix A for the linear transformation T. (2) Determine whether there exists x € R² such that T(x) = b. Problem 4.2. Consider the following matrices # Compute the following: (1) AT; A -1-2 -2 -2 1 (2) BT; Let b (3) A-2BT. 11 3 5 11 + 1₂ Problem 4.1. Define T: R2 R³ by T(x)=₁-2r₂ for all x = [2x₁ -2] -D- (1) Find the standard matrix A for the linear transformation T. (2) Determine whether there exists x € R² such that T(x) = b. Problem 4.2. Consider the following matrices # Compute the following: (1) AT; A -1-2 -2 -2 1 (2) BT; Let b (3) A-2BT. 11 3 5