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Determine Matrix Mapping
la-01-01
multiple
972
randRangeExclude(-5,5,[0]) randRangeExclude(-5,5,[0]) randRangeExclude(-5,5,[0]) randRangeExclude(-4,4,[0,1-A])

Given the vector v.

For which entries does the matrix A = \begin{pmatrix} \color{red}{a} & D \\ 0 & \color{blue}{b} \end{pmatrix} fit the situation below, if the second vector \color{orange} A\cdot v is?



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a \color{red}a = A
b \color{blue}b = B

Find the entries \color{red}{a} and \color{blue}{b} with A \cdot \begin{pmatrix} C \\ C \end{pmatrix} = \color{orange}\begin{pmatrix} C*A+D*C \\ C*B \end{pmatrix}.

Initially, this is the equation \begin{pmatrix} \color{red}{a} & D \\ 0 & \color{blue}{b} \end{pmatrix} \cdot \begin{pmatrix} C \\ C \end{pmatrix} = \begin{pmatrix} negParens(C) \cdot {\color{red}a} + C \cdot negParens(D) \\ negParens(C) \cdot \color{blue}{b} \end{pmatrix} = \color{orange} \begin{pmatrix} C*A+D*C \\ C*B \end{pmatrix}.

In the two coordinates, the two equations are negParens(C) \cdot {\color{red}a} + negParens(C) \cdot negParens(D) = \color{orange} C*A+D*C and negParens(C) \cdot {\color{blue}b} = \color{orange}C*B

therefore {\color{red}a} = A and {\color{blue}b} = B.