Linear Algebra Examples

$A [\begin{array}{c} a \\ b \\ c \end{array}] + B [\begin{array}{c} d \\ e \\ f \end{array}]$

Step 1

Simplify each term.

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Step 1.1

Multiply $A$ by each element of the matrix.

$[\begin{array}{c} A a \\ A b \\ A c \end{array}] + B [\begin{array}{c} d \\ e \\ f \end{array}]$

Step 1.2

Multiply $B$ by each element of the matrix.

$[\begin{array}{c} A a \\ A b \\ A c \end{array}] + [\begin{array}{c} B d \\ B e \\ B f \end{array}]$

Step 2

Add the corresponding elements.

$[\begin{array}{c} A a + B d \\ A b + B e \\ A c + B f \end{array}]$