Given the linear transformation T : R R: X1 *([:D)-[ T = X3 a) Find...

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Given the linear transformation T : R³ → R²: X1 *([:D)-[ T = X3 a) Find the standard matrix representation of T. x1 - 5x2 - 7x3 −3x₁ + 7x₂ + 5x3 -2 -2 b) Find a vector x whose image under T is b = c) Is T onto R²? Is T one-to-one? Is T invertible? Explain. Given the linear transformation T : R³ → R²: X1 *([:D)-[ T = X3 a) Find the standard matrix representation of T. x1 - 5x2 - 7x3 −3x₁ + 7x₂ + 5x3 -2 -2 b) Find a vector x whose image under T is b = c) Is T onto R²? Is T one-to-one? Is T invertible? Explain.