Question

Let B and C be two ordered bases of R^3, and consider a linear transformation T: R^3 -> R^3. Suppose that the change of base matrix I_C,B is given by [1 -2 2] [-3 -1 -1] [1 -3 1] and the coordinate matrix T_C,C of T with respect to C is given by [2 0 -2] [-1 -3 -1] [0 -3 1]. Use this to determine coordinate matrix T_B,B of T with respect to B!

          Let B and C be two ordered bases of R^3, and consider a linear transformation T: R^3 -> R^3. Suppose that the change of base matrix I_C,B is given by
[1 -2 2]
[-3 -1 -1]
[1 -3 1]
and the coordinate matrix T_C,C of T with respect to C is given by
[2 0 -2]
[-1 -3 -1]
[0 -3 1].
Use this to determine coordinate matrix T_B,B of T with respect to B!

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Let B and C be two ordered bases of R^3, and consider a linear transformation T: R^3 -> R^3. Suppose that the change of base matrix IC,B is given by
[1 -2 2]
[-3 -1 -1]
[1 -3 1]
and the coordinate matrix TC,C of T with respect to C is given by
[2 0 -2]
[-1 -3 -1]
[0 -3 1].
Use this to determine coordinate matrix TB,B of T with respect to B!

Added by Meghan L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

05/29/2022

Step 1

Step 1: Find the change of basis matrix [I]B,C using the formula [I]B,C = ([I]C,B)^(-1) Show more…

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Let B and C be two ordered bases of R3, and consider a linear transformation T: R3 -> R3. Suppose that the change of base matrix [I]c,B is given by and the coordinate matrix [T]c,c of T with respect to C is given by Use this to determine the coordinate matrix [T]B,B of T with respect to B!

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