Show all steps clearly, thanks. Let T(x,y,z) = (x + y,y + z,x + z). Determine if
ID: 2901900 • Letter: S
Question
Show all steps clearly, thanks.
Let T(x,y,z) = (x + y,y + z,x + z). Determine if T is invertible. If it is, find its inverse. Find the standard matrices for T = T2 and T1 = T1 T2 where, Let B = {(1, 1), (-2, 3)} and B' = {(1,-1),(0,1)} be bases for R2, and let be the matrix for T: R2 -> R2 relative to B. Find the transition matrix P from B' to B. Use the matrices A and P to find [v]B and [T(v)]B where [v]B = Find A (the matrix of T relative to B) and P -1. Find [T(v)]B in two ways: first as P-1[T(v)]B and then as A'[v]B. Consider the pair of rotations: 45degreeabout the y-axis followed by 90degreeabout the z-axis. Determine the matrix that produces this pair of rotations. Find the image of the v = (1, -1, 2) under these rotations.Explanation / Answer
1.
T is invertible
T^-1(x,y,z) = ((-x+y+z)/2, (x-y+z)/2, (x+y-z)/2)
2.
T(x,y) = T2oT1(x,y) = T2(x,y,y) = (y,y)
=>
T =
[0 1
0 1]
T' = T1oT2(x,y,z) = T1(y,z) = (y,z,z)
=>
T'
[0 1 0
0 0 1
0 0 1]