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- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/A_First_Journey_Through_Linear_Algebra/06%3A_Linear_Transformations/6.01%3A_Linear_TransformationsRecall that when we multiply an m×n matrix by an n×1 column vector, the result is an m×1 column vector. In this section we will discuss how, through matrix multiplication, an m×n matrix transf...Recall that when we multiply an m×n matrix by an n×1 column vector, the result is an m×1 column vector. In this section we will discuss how, through matrix multiplication, an m×n matrix transforms an n×1 column vector into an m×1 column vector.
- https://math.libretexts.org/Courses/Irvine_Valley_College/Math_26%3A_Introduction_to_Linear_Algebra/02%3A_Linear_Transformations_and_Matrix_Algebra/2.02%3A_Linear_Transformations/2.2.02%3A_Matrix_Representations\[\left.\begin{aligned} T(\vec{e}_1)&=T\left(\left[\begin{array}{c}1\\0\end{array}\right]\right)=\left[\begin{array}{c}3(1)-0\\0\\1\end{array}\right]=\left[\begin{array}{c}3\\0\\1\end{array}\right] \\...\[\left.\begin{aligned} T(\vec{e}_1)&=T\left(\left[\begin{array}{c}1\\0\end{array}\right]\right)=\left[\begin{array}{c}3(1)-0\\0\\1\end{array}\right]=\left[\begin{array}{c}3\\0\\1\end{array}\right] \\ T(\vec{e}_2)&=T\left(\left[\begin{array}{c}0\\1\end{array}\right]\right)=\left[\begin{array}{c}3(0)-1\\1\\0\end{array}\right]=\left[\begin{array}{c}-1\\1\\0\end{array}\right]\end{aligned}\right\}\implies A=\left[\begin{array}{cc}3&-1\\0&1\\1&0\end{array}\right]\nonumber\]
- https://math.libretexts.org/Bookshelves/Linear_Algebra/A_First_Course_in_Linear_Algebra_(Kuttler)/05%3A_Linear_Transformations/5.01%3A_Linear_TransformationsRecall that when we multiply an m×n matrix by an n×1 column vector, the result is an m×1 column vector. In this section we will discuss how, through matrix multiplication, an m×n matrix transf...Recall that when we multiply an m×n matrix by an n×1 column vector, the result is an m×1 column vector. In this section we will discuss how, through matrix multiplication, an m×n matrix transforms an n×1 column vector into an m×1 column vector.
- https://math.libretexts.org/Courses/Mission_College/MAT_04C_Linear_Algebra_(Kravets)/04%3A_Linear_Transformations/4.01%3A_Linear_TransformationsRecall that when we multiply an m×n matrix by an n×1 column vector, the result is an m×1 column vector. In this section we will discuss how, through matrix multiplication, an m×n matrix transf...Recall that when we multiply an m×n matrix by an n×1 column vector, the result is an m×1 column vector. In this section we will discuss how, through matrix multiplication, an m×n matrix transforms an n×1 column vector into an m×1 column vector.
- https://math.libretexts.org/Courses/Reedley_College/Differential_Equations_and_Linear_Algebra_(Zook)/05%3A_Linear_Transformations/5.01%3A_Linear_TransformationsRecall that when we multiply an m×n matrix by an n×1 column vector, the result is an m×1 column vector. In this section we will discuss how, through matrix multiplication, an m×n matrix transf...Recall that when we multiply an m×n matrix by an n×1 column vector, the result is an m×1 column vector. In this section we will discuss how, through matrix multiplication, an m×n matrix transforms an n×1 column vector into an m×1 column vector.
