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Update index.mdx (#414)
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Just changed the A21 element of the array.
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parth10-1 committed Apr 9, 2024
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Expand Up @@ -243,7 +243,7 @@ If you're given a 2x2 matrix describing a linear transformation, and a specific
image="./figures/matrices/MatrixNotation2x2InputOutput.svg"
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When you do this super generally, with a matrix that has entries $\left[\begin{array}{cc}a & b \\c & d\end{array}\right]$, and a vector $\left[\begin{array}{c} x \\ y \end{array}\right]$, what's the resulting vector? Remember here that the first column $\left[\begin{array}{c} a \\ b \end{array}\right]$ corresponds to the place where the first basis vector lands, and the second column $\left[\begin{array}{c} b \\ d \end{array}\right]$ is the place where the second basis vector lands.
When you do this super generally, with a matrix that has entries $\left[\begin{array}{cc}a & b \\c & d\end{array}\right]$, and a vector $\left[\begin{array}{c} x \\ y \end{array}\right]$, what's the resulting vector? Remember here that the first column $\left[\begin{array}{c} a \\ c \end{array}\right]$ corresponds to the place where the first basis vector lands, and the second column $\left[\begin{array}{c} b \\ d \end{array}\right]$ is the place where the second basis vector lands.

Well, it will be $x \left[\begin{array}{c} a \\ c \end{array}\right] + y \left[\begin{array}{c} b \\ d \end{array}\right]$ and, putting this together, you get a vector $\left[\begin{array}{c} ax + by \\ cx + dy \end{array}\right]$.

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