Matrices

Matrices are mathematical concept that expresses numbers, letters and symbols in rows and columns

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Addition of Matrices

Add the matrices A + B

A = $\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ \mathrm{c}& \mathrm{d}\end{array}\right]$ + B = $\left[\begin{array}{cc}\mathrm{e}& \mathrm{f}\\ \mathrm{g}& \mathrm{h}\end{array}\right]$

A + B = $\left[\begin{array}{cc}\mathrm{a\; +\; e}& \mathrm{b\; +\; f}\\ \mathrm{c\; +\; g}& \mathrm{d\; +\; h}\end{array}\right]$

Example 1

Find the value of the following matrices

(a) A + B

(b) B + C

Solutions:

(a) A + B

A = $\left[\begin{array}{cc}5& 3\\ 1& 6\end{array}\right]$ B = $\left[\begin{array}{cc}2& 9\\ 10& 7\end{array}\right]$

A + B = $\left[\begin{array}{cc}\mathrm{5\; +\; 2}& \mathrm{3\; +\; 9}\\ \mathrm{1\; +\; 10}& \mathrm{6\; +\; 7}\end{array}\right]$

Answer: A + B = $\left[\begin{array}{cc}7& 12\\ 11& 13\end{array}\right]$

(b) B + C

B = $\left[\begin{array}{cc}2& 9\\ 10& 7\end{array}\right]$ C = $\left[\begin{array}{cc}4& 0\\ 1& 8\end{array}\right]$

B + C = $\left[\begin{array}{cc}\mathrm{2\; +\; 4}& \mathrm{9\; +\; 0}\\ \mathrm{10\; +\; 1}& \mathrm{7\; +\; 8}\end{array}\right]$

Answer: B + C = $\left[\begin{array}{cc}6& 9\\ 11& 15\end{array}\right]$

Subtraction of matrices

Subtraction A - B

A = $\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ \mathrm{c}& \mathrm{d}\end{array}\right]$ - B = $\left[\begin{array}{cc}\mathrm{e}& \mathrm{f}\\ \mathrm{g}& \mathrm{h}\end{array}\right]$

A - B = $\left[\begin{array}{cc}\mathrm{a\; -\; e}& \mathrm{b\; -\; f}\\ \mathrm{c\; -\; g}& \mathrm{d\; -\; h}\end{array}\right]$

Example 2

Find the value of the following matrices

A - B

A = $\left[\begin{array}{cc}5& 3\\ 1& 6\end{array}\right]$ B = $\left[\begin{array}{cc}2& 9\\ 10& 7\end{array}\right]$

A - B = $\left[\begin{array}{cc}\mathrm{5\; -\; 2}& \mathrm{3\; -\; 9}\\ \mathrm{1\; -\; 10}& \mathrm{6\; -\; 7}\end{array}\right]$

Answer: A - B = $\left[\begin{array}{cc}3& -6\\ -9& -1\end{array}\right]$

Multiplication of matrices

Find the multiplication of A X B

A = $\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ \mathrm{c}& \mathrm{d}\end{array}\right]$ B = $\left[\begin{array}{cc}\mathrm{e}& \mathrm{f}\\ \mathrm{g}& \mathrm{h}\end{array}\right]$

A X B = $\left[\begin{array}{cc}\mathrm{a\; \times \; e\; +\; b\; \times \; g}& \mathrm{a\; \times \; f\; +\; b\; \times \; h}\\ \mathrm{c\; \times \; e\; +\; d\; \times \; g}& \mathrm{c\; \times \; f\; +\; d\; \times \; h}\end{array}\right]$

Example 3

Find the matrices A X B

A = $\left[\begin{array}{cc}5& 3\\ 1& 6\end{array}\right]$ B = $\left[\begin{array}{cc}2& 9\\ 10& 7\end{array}\right]$

A X B = $\left[\begin{array}{cc}\mathrm{5\; \times \; 2\; +\; 3\; \times \; 10}& \mathrm{5\; \times \; 9\; +\; 3\; \times \; 7}\\ \mathrm{1\; \times \; 2\; +\; 6\; \times \; 10}& \mathrm{1\; \times \; 9\; +\; 6\; \times \; 7}\end{array}\right]$

A X B = $\left[\begin{array}{cc}\mathrm{10\; +\; 30}& \mathrm{45\; +\; 21}\\ \mathrm{2\; +\; 60}& \mathrm{9\; +\; 42}\end{array}\right]$

Answer: A X B = $\left[\begin{array}{cc}40& 66\\ 62& 51\end{array}\right]$

Transpose and multiplication of matrices

How to Find inverse of a matrix and its determinant