[ANSWER] MAT350 5.8 MATLAB: Change of Bases

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MAT350 5.8 MATLAB: Change of Bases

Create the augmented matrix D, whose columns are the ordered basis of C followed by the image of the ordered basis of B.

D = [1 2 3 7; 4 3 -1 -1]

Row reduce the augmented matrix to get [I | T_BtoC].  Use “format rat” to view values as rational numbers, if desired.

temp = rref(D)

format rat

T_BtoC = temp(:,3:4)

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MAT350 5.8 MATLAB: Change of Bases

Create the augmented matrix D, whose columns are the ordered basis of C followed by the image of the ordered basis of B.

D = [1 2 3 7; 4 3 -1 -1]

Row reduce the augmented matrix to get [I | T_BtoC].  Use “format rat” to view values as rational numbers, if desired.

temp = rref(D)

format rat

T_BtoC = temp(:,3:4)

 

For this actvity, find the matrix represenatation [T]C B  for the linear transformation defined by R2 -> R3

 

x1         x1 + x2

T ( [ x2 ] ) = [ -2×3    ]

x3

 

with respect

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to the ordered bases

 

1        0       4                     3        2

B =  { [ 0 ] , [ -3 ] , [ 1 ] }         C = { [ -1 ] , [ 5 ] }

1        2       0

 

Create the augmented matrix D, whose columns are the ordered basis of C followed by the image of the ordered basis of B.

D = [3 2 1 -3 5; -1 5 -2 -4 0]

Row reduce the augmented matrix to get [I | T_BtoC].  Store the transformation matrix in T_BtoC.

E = rref (D);

T_BtoC = E (:,3:5);

Related; MAT350 5.2 MATLAB: Linear Transformations.

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