Find the vector mathbfx determined by the coordinate vector [mathbfx]b | Mathematics II 2076

Mathematics II20765 marksNumerical: vector from coordinate vectorCoordinate systems

Find the vector $\mathbf{x}$ determined by the coordinate vector $[\mathbf{x}]_\beta = \begin{bmatrix} -4 \\ 8 \\ 7 \end{bmatrix}$ where $\beta = \left\{ \begin{bmatrix} -1 \\ 2 \\ 0 \end{bmatrix}, \begin{bmatrix} 3 \\ -5 \\ 2 \end{bmatrix}, \begin{bmatrix} 4 \\ -7 \\ 3 \end{bmatrix} \right\}$ . [5]

Find the vector $\mathbf{x}$ determined by the coordinate vector $[\mathbf{x}]_\beta = \begin{bmatrix} -4 \ 8 \ 7 \end{bmatrix}$ where $\beta = \left{ \begin{bmatrix} -1 \ 2 \ 0 \end{bmatrix}, \begin{bmatrix} 3 \ -5 \ 2 \end{bmatrix}, \begin{bmatrix} 4 \ -7 \ 3 \end{bmatrix} \right}$. [5]

Basis: $\mathbf{b}1 = \begin{bmatrix} -1 \\ 2 \\ 0 \end{bmatrix}, \quad \mathbf{b}2 = \begin{bmatrix} 3 \\ -5 \\ 2 \end{bmatrix}, \quad \mathbf{b}3 = \begin{bmatrix} 4 \\ -7 \\ 3 \end{bmatrix}$ Coordinate vector: $$[\mathbf{x}]\beta = \begin{bmatrix} -4 \ 8 \ 7 \end{bmatrix} \Rightarrow c1 = ...

Basis: $$\mathbf{b}1 = \begin{bmatrix} -1 \ 2 \ 0 \end{bmatrix}, \quad \mathbf{b}2 = \begin{bmatrix} 3 \ -5 \ 2 \end{bmatrix}, \quad \mathbf{b}3 = \begin{bmatrix} 4 \ -7 \ 3 \end{bmatrix}$$ Coordinate vector: $$[\mathbf{x}]\beta = \begin{bmatrix} -4 \ 8 \ 7 \end{bmatrix} \Rightarrow c1 = ...

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Find the vector mathbfx determined by the coordinate vector [mathbfx]beta = beginbmatrix -4 8 7 endbmatrix where beta = left beginbmatrix -1 2 0 endbmatrix, beginbmatrix 3 -5 2 endbmatrix, beginbmatrix 4 -7 3 endbmatrix right.