The given T is a linear transformation from R² into R². Show that T is invertible and find a formula for T1. T(x₁,x₂) = (4x₁ - 5x2, − 4x₁ + 1 -7x₂) To show that T is invertible, calculate the determinant of the standard matrix for T. The determinant of the standard matrix is (Simplify your answer.)

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The given T is a linear transformation from R² into R². Show that T is invertible and find a formula for T¹. T(x1,x2) = (6x₁-9x2,- 6x₁ +5x₂) To show that T is invertible, calculate the determinant of the standard matrix for T. The determinant of the standard matrix is (Simplify your answer.)

a []·. and 0, and compute the determinants of the matrices [u v] and [vu]. Draw a picture and explain what you find. Let u = C [:] , where a, b, and c are positive (for simplicity). Compute the area of the parallelogram determined by u, v, u + v, 0 and v= The area of the parallelogram determined by u, v, u + v, and 0 is (Simplify your answer.)