Math Problem Statement
Given the basis C, the change of basis matrix P_C<-B, and [x]_B. Determine x:
Let C be a basis that contains vectors: [2, 2, 1, 2], [1, 2, 2, 2], [1, 1, 2, -1], [1, -1, 2, 2], P_C<-B = [-2 2 1 -2, 2 4 -2 2, 4 1 1 -1, -1 2 -1 -2, and [x]_B = [2, -1, -1, -1]. then :
x = [?, ?, ?, ?]
the answer is not [-5, 0, 7, -1]
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Change of Basis
Matrix Multiplication
Coordinate Systems
Formulas
x = P_{C <- B} [x]_B
Matrix multiplication: A * B
Theorems
Change of Basis Theorem
Matrix-Vector Multiplication Theorem
Suitable Grade Level
Undergraduate Linear Algebra