Mathegoras

Vectors and matrices › Rank, eigenvalues and linear maps › Coordinates in a basis

Decomposing a vector in a basis

High school · ●●○○○ 20 pts

Write the vector x=(−5,−5,5)x=(-5, -5, 5) as a linear combination of p=(−2,0,1)p=(-2, 0, 1), q=(1,3,−1)q=(1, 3, -1) and r=(0,4,1)r=(0, 4, 1), that is, find α\alpha, β\beta, γ\gamma with x=αp+βq+γrx=\alpha p+\beta q+\gamma r.

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linear combinationsvector decompositionsystems of linear equations