The given T is a linear transformation from R² into R2. Show that T is invertible and find a formula for T-1 T(x₁.x2) =

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The Given T Is A Linear Transformation From R Into R2 Show That T Is Invertible And Find A Formula For T 1 T X X2 1 (17.9 KiB) Viewed 46 times

The Given T Is A Linear Transformation From R Into R2 Show That T Is Invertible And Find A Formula For T 1 T X X2 2 (35.54 KiB) Viewed 46 times

The given T is a linear transformation from R² into R2. Show that T is invertible and find a formula for T-1 T(x₁.x2) = (4x₁-6x₂.-4x₁ +9x2) 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.) T-¹ (X₁X2) = (Type an ordered pair. Type an expression using x, and x₂ as the variables.)
Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(X1 X2 X3 X4) = (x2 + x3 x3 +X41X2 + x3,0) a. Is the linear transformation one-to-one? A. T is one-to-one because T(x)=0 has only the trivial solution. B. T is one-to-one because the column vectors are not scalar multiples of each other. C. T is not one-to-one because the columns of the standard matrix A are linearly independent. D. T is not one-to-one because the standard matrix A has a free variable. b. Is the linear transformation onto? A. T is not onto because the fourth row of the standard matrix A is all zeros. B. T is onto because the standard matrix A does not have a pivot position for every row. C. T is onto because the columns of the standard matrix A span R4. D. T is not onto because the columns of the standard matrix A span R4