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To multiply a matrix on scalar, multiply each element $a_{ij}$ of the matrix on this scalar: | To multiply a matrix on scalar, multiply each element $a_{ij}$ of the matrix on this scalar: | ||
− | + | <math>A = \begin{bmatrix} | |
a_{11} & a_{12} & \cdots & a_{1n}\\ | a_{11} & a_{12} & \cdots & a_{1n}\\ | ||
a_{21} & a_{22} & \cdots & a_{2n}\\ | a_{21} & a_{22} & \cdots & a_{2n}\\ | ||
\vdots & \vdots & \ddots & \vdots \\ | \vdots & \vdots & \ddots & \vdots \\ | ||
a_{m1} & a_{m2} & \cdots & a_{mn} | a_{m1} & a_{m2} & \cdots & a_{mn} | ||
− | \end{bmatrix} | + | \end{bmatrix} |
− | + | </math>, then | |
+ | <math>c \cdot A \begin{bmatrix} | ||
c \cdot a_{11} & c \cdot a_{12} & \cdots & c \cdot a_{1n}\\ | c \cdot a_{11} & c \cdot a_{12} & \cdots & c \cdot a_{1n}\\ | ||
c \cdot a_{21} & c \cdot a_{22} & \cdots & c \cdot a_{2n}\\ | c \cdot a_{21} & c \cdot a_{22} & \cdots & c \cdot a_{2n}\\ | ||
\vdots & \vdots & \ddots & \vdots \\ | \vdots & \vdots & \ddots & \vdots \\ | ||
c \cdot a_{m1} & c \cdot a_{m2} & \cdots & c \cdot a_{mn} | c \cdot a_{m1} & c \cdot a_{m2} & \cdots & c \cdot a_{mn} | ||
− | \end{bmatrix} | + | \end{bmatrix}</math> |
A Matrix can be multiplied
To multiply a matrix on scalar, multiply each element $a_{ij}$ of the matrix on this scalar:
[math]A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n}\\ a_{21} & a_{22} & \cdots & a_{2n}\\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix} [/math], then [math]c \cdot A \begin{bmatrix} c \cdot a_{11} & c \cdot a_{12} & \cdots & c \cdot a_{1n}\\ c \cdot a_{21} & c \cdot a_{22} & \cdots & c \cdot a_{2n}\\ \vdots & \vdots & \ddots & \vdots \\ c \cdot a_{m1} & c \cdot a_{m2} & \cdots & c \cdot a_{mn} \end{bmatrix}[/math]