Maria C. answered • 11/05/22
25+ years of teaching, tailored to your learning style
Let T be the linear transformation defined by T(x, y) = (5x, 8x − 3y, 7x + 2y, −x - 6y). Find its associated matrix A.
T is a linear transformation from R2 to R4, T: R2->R4.
The associated matrix A is a matrix such that for all vectors x in R2, T(x)=Ax
A is a 4x2 matrix. To find it, we compute T at the standard basis for R2.
T(e1) = T(1,0) = (5, 8, 7, −1)
T(e2) = T(0,1) = (0, -3, 2, −6)
T(e1) will be the 1st column of A and T(e2) will be the 2nd column of A.
A = [5 0
8 -3
7 2
-1 -6]
We double-check that, indeed, this is true (that we did not make any mistakes anywhere)
A*(x,y) =
[5 0
8 -3
7 2
-1 -6] *(x,y) = (5x,8x-3y,7x+2y,-x-6y)
Done.
I hope this helps! Please let me know if you have any questions. Good luck, Maria
Emin T.
Let T: R²→ R³ be the linear transformation defined by T(x, y) = (3x − y, 5x + 5y, y — 5x). Find a vector w that is not in the image of T.11/05/22
Emin T.
i have two questions could you check it? Determine which of the following functions are onto. A) f: R → R defined by f(x) = x³ + x. B) f: R³→R³ defined by f(x, y, z) = (x − y, yz, xz). C) f: R → R defined by f(x) = x². D) f: R → R defined by f(x) = x³. E) f: R³→ R³ defined by f(x, y, z) = (x + y, y+z, x+2).11/05/22