52. Consider a 2 x 2 matrix A = b d with column vectors v= = [a] and w= We define the linear transformation T(x) = det [

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52 Consider A 2 X 2 Matrix A B D With Column Vectors V A And W We Define The Linear Transformation T X Det 1 (41.51 KiB) Viewed 26 times

52. Consider a 2 x 2 matrix A = b d with column vectors v= = [a] and w= We define the linear transformation T(x) = det [x] det [x] from R² to R². a. Find the standard matrix B of T. (Write the entries of B in terms of the entries a, b, c, d of A.) b. What is the relationship between the determinants of A and B? c. Show that BA is a scalar multiple of 12. What about AB? d. If A is noninvertible (but nonzero), what is the rela- tionship between the image of A and the kernel of B? What about the kernel of A and the image of B? e. If A is invertible, what is the relationship between B and A-1? a = [² -4.