(1 point) Consider the ordered bases B = ((7,-8), (-6,7)) and C = ((2,-4), (3,-3
ID: 3116226 • Letter: #
Question
(1 point) Consider the ordered bases B = ((7,-8), (-6,7)) and C = ((2,-4), (3,-3)) for the vector space R a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)) b. Find the transition matrix from B to E c. Find the transition matrix from E to B d. Find the transition matrix from C to B e. Find the coordinates of u = (-3,-3) in the ordered basis B. Note that [u]B-7 [11]E- [4]B = f. Find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]c (2,-1)Explanation / Answer
a.The transition matrix from C to the standard ordered basis E is TCE=
2
3
-4
-3
b. The transition matrix from B to the standard ordered basis E is TBE =
7
-6
-8
7
c. Let M1 =
7
-6
1
0
-8
7
0
1
The RREF of M1is
1
0
7
6
0
1
8
7
Then the transition matrix from the standard ordered basis E to B is TEB =
7
6
8
7
d. Let M2 =
7
-6
2
3
-8
7
-4
-3
The RREF of M2is
1
0
-10
3
0
1
-12
3
Then the transition matrix from the ordered basis C to B is TCB =
-10
3
-12
3
e. Let P =
7
-6
-3
-8
7
-3
The RREF of P is
1
0
-39
0
1
-45
Then [u]B = (-39,-45)T.
f. We have v = 2(2,-4)-1(3,-3) = (1,-5). Let Q =
7
-6
1
-8
7
-5
The RREF of Q is
1
0
-23
0
1
-27
Then [v]B =(-23,-27)T.
2
3
-4
-3
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