This app illustrates the effect of a matrix transformation of R^2 via column vectors of the matrix telling us how the matrix transforms the standard basis of R^2.

default-2023

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input_1

input_2

input_3

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mn>1</mn></msub><mo>=</mo></mrow><annotation encoding="application/x-tex">e_1 = </annotation></semantics></math>e1​=﻿ {{ "\\begin{bmatrix} 1\\\\ 0\\ \\end{bmatrix}" | katex }} ﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mn>2</mn></msub><mo>=</mo></mrow><annotation encoding="application/x-tex">e_2 = </annotation></semantics></math>e2​=﻿ {{ "\\begin{bmatrix} 0\\\\ 1\\ \\end{bmatrix}" | katex }}

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><msub><mi>e</mi><mn>1</mn></msub><mo>=</mo></mrow><annotation encoding="application/x-tex">Me_1 =</annotation></semantics></math>Me1​=﻿ ﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mo>∗</mo></mrow><annotation encoding="application/x-tex">M * </annotation></semantics></math>M∗﻿ {{ "\\begin{bmatrix} 1 \\\\ 0\\ \\end{bmatrix}" | katex }}﻿﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><msub><mi>e</mi><mn>2</mn></msub><mo>=</mo></mrow><annotation encoding="application/x-tex">Me_2 = </annotation></semantics></math>Me2​=﻿ ﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mo>∗</mo></mrow><annotation encoding="application/x-tex">M * </annotation></semantics></math>M∗﻿ {{ "\\begin{bmatrix} 0 \\\\ 1\\ \\end{bmatrix}" | katex }}

Choose a matrix of ﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="normal">R</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">ℝ^2</annotation></semantics></math>R2﻿ to be used in transforming the standard basis of ﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="normal">R</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">ℝ^2</annotation></semantics></math>R2﻿ using column vectors ﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">e_1</annotation></semantics></math>e1​﻿ and ﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">e_2</annotation></semantics></math>e2​﻿.

Matrix Transformation of R^2 Via Column Vectors

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