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Linear algebra(linear transformation)

  • Thread starter chuy52506
  • Start date
  • #1
77
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Homework Statement


Let B={[1,1]T,[1,2]T} be a basis of R2.
Suppose T[tex]\in[/tex]L(R2,R2) with [T]B=
|1 2|
|3 4|



Homework Equations


Find T([4,3]T)


The Attempt at a Solution


I augmenting matrix A such that [A|[T]B]
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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Why augmenting? The way you have written that you are just asked to find the matrix product
[tex]\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\begin{bmatrix}4 \\ 3\end{bmatrix}[/tex]
 
  • #3
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Remember, the columns in the matrix representation of T are just the image of the basis vectors. That is [T]B =

[tex]
\left(\begin{array}{cc} | & | \\ T(v_1) & T(v_2) \\ | & | \end{array}\right)
[/tex]

Use this and then write (4,3) as a linear combination of the basis vectors.
 
  • #4
77
0
then would it be
|1| + |1|
|1|*4 + |2|*3= answer?
 

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