Lecture 03

01. Matrix Multiplication (4 ways)

02. Inverse Matrix

03. Gaussian - Jordan Method (find inverse matrix)

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01. Matrix Multiplication (4 ways)

a. Element Way

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b. Column Way

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Columns of C is combination of columns of A.

c. Row Way

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Rows of C is combination of rows of B

d. Matrix Overlay

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e.Block Way

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Divide A and B into blocks. Notice that the element of A and B is sub matrix and the counterpart of C is also sub matrix with corresponding shape. The element way still stands for matrix multiplication in blocks.

02. Inverse Matrix

a. Definition

The inverse matrix of squared matrix A is a matrix that has property below.

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b.Singular

For a matrix A, if there exists a non zero vector s.t. Ax = 0, then A is singular and has no inverse matrix.

singular_proof.png

03. Gaussian - Jordan Method (find inverse matrix)

Gaussian_Jordan.png