2 0 -1 1 |1 4. Suppose T is a linear transformation with matrix A 2...
QUESTION 1. §1.9 THE MATRIX OF A LINEAR TRANSFORMATION Le t T R be the linear transformation defined by t-th AnSwer Find the standard matrix of T. Is T one to one? Is T onto? Jushif'cahon
Question 8 [10 points] Suppose T: RM22 is a linear transformation whose action on a basis for R4 is as follows -1 1 -11 4 4 0 1 1 0 1 -1 1 -45 1 2-2 1 -1 7 0 Determine whether T is one-to-one andlor onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is yt onto, show this by providing a matrix in M22 that is...
Recall that if T: R" R" is a linear transforrmation T(x) = [Tx, where [T is the transformation matrix, then 1. ker(T) null([T] (ker(T) is the kernel of T) 2. T is one-to-one exactly when ker(T) = {0 3. range of T subspace spanned by the columns of [T] col([T) 4. T is onto exactly when T(x) = [Tx = b is consistent for all b in R". 5. Also, T is onto exactly when range of T col([T]) =...
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto
Suppose T: M2,2 P2 is a linear transformation whose action is defined by s and that we have the ordered bases 1 00 1 0 000 0 00 010 0 1 D-1x2 for M2.2 and P2 respectively. a) Find the matrix of T corresponding to the ordered bases B and D MD(T) 0 0 0 b) Use this matrix to determine whether T is one-to-one or onto < Select an answer >, < Select an answer >
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation T: that first reflects points through the horizontal L-axis and then reflects points - through the vertical y-axis. 2. Show that the linear transformation T: R - R whose standard [ 2011 matrix is A= is onto but not one-to-one. - R$ whose standard 3. Show that the linear transformation T: R 0 1 matrix is A = 1 1 lov Lool is one-to-one...
1 4 bea linear/matrix transformation such that Let T: 3 Fi 1 4 1 T 1 1 C 6 h 3 Use the fact that T is linear to find the standard matrix [T of T and find T 1 Find a match for each of the following questions or choose NO MATCH if you can't find a match. What is the domain of T? What is the codomain of T? 4 4 How many rows does [T] have? How...
5. (8 pts) Suppose B is a 4 x 5 matrix, and the associated linear transformation T(E) Bd, is onto. (a) (3) Find dim Nul(B) (b) (2) Does Ba 5 have a unique solution for every B (c) (3) Give a geometric interpretation to the solution set of Bt- 0 5. (8 pts) Suppose B is a 4 x 5 matrix, and the associated linear transformation T(E) Bd, is onto. (a) (3) Find dim Nul(B) (b) (2) Does Ba 5...
1. (8 pts.) Suppose T is a linear transformation and -(1)-(C). --- () - 0 Solve the matrix vector equations below. Explain 2. (8 pts.) Below are a matrix A, its inverse, and a vector b. 1983--013... (1) A = A-1 = 1-4 3 2 -5 7 2 0 1) , and b = x) Determine the value of x. Then solve the matrix vector equation Av = b. [-u-5 il 14 s1 3 70 | 71-3-70 12 x 12...
need help on this. thanks in advance Question 16 Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 1-23 -1 3-4 2 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R. One-to-one; not onto #3 One-to-one; onto a Not one-to-one; onto R3 Not one-to-one; not onto a