Question

Let B={b1, b2}, C={c1, c2}. (B and C are both bases for R^2, you don't need to check this.) Find a change of coordinates matrix from B to C. Also, suppose that x = 2b1 - 3b2. Express x as a vector in the standard basis, basis B, and basis C. b1 = (-3, 2), b2 = (1, -1) c1 = (-1, 4), c2 = (2, -7)

          Let B={b1, b2}, C={c1, c2}. (B and C are both bases for R^2, you don't need to check this.) Find a change of coordinates matrix from B to C.

Also, suppose that x = 2b1 - 3b2. Express x as a vector in the standard basis, basis B, and basis C.

b1 = (-3, 2), b2 = (1, -1)
c1 = (-1, 4), c2 = (2, -7)

Let B=b1, b2, C=c1, c2. (B and C are both bases for R^2, you don't need to check this.) Find a change of coordinates matrix from B to C.

Also, suppose that x = 2b1 - 3b2. Express x as a vector in the standard basis, basis B, and basis C.

b1 = (-3, 2), b2 = (1, -1)
c1 = (-1, 4), c2 = (2, -7)

Added by Chad C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/08/2023

Step 1

** To find the change of coordinates matrix from B to C, we need to express each vector in basis B as a linear combination of vectors in basis C. Let's start with $b_1$: * We want to find scalars $x$ and $y$ such that: $b_1 = x c_1 + y c_2$ * Substitute Show more…

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Let B = {b1, b2}, C = {c1, c2}. (B and C are both bases for R2, you don't need to check this). Find a change of coordinates matrix from B to C. Also, suppose that X = 2b1 + 3b2. Express X as a vector in the standard basis, basis B, and basis C. b1 = [3, 0], b2 = [2, -1] c1 = [4, 1], c2 = [0, 2]