A = $\left( \begin{array} { l l } a _ { 11 } & a _ { 12 } \\a _ { 21 } & a _ { 22 }\end{array} \right)$

question 18

Essay

A = $\left( \begin{array} { l l } a _ { 11 } & a _ { 12 } \\a _ { 21 } & a _ { 22 }\end{array} \right)$ , B = $\left( \begin{array} { l l } b _ { 11 } & b _ { 12 } \\b _ { 21 } & b _ { 22 }\end{array} \right)$ , and C = $\left( \begin{array} { l l l } c _ { 11 } & c _ { 12 } & c _ { 13 } \\c _ { 21 } & c _ { 22 } & c _ { 23 }\end{array} \right)$ show that $( A + B ) ^ { \prime }$ = $A ^ { \prime }$ + $B ^ { \prime }$ and $( A C ) ^ { \prime }$ = $C ^ { \prime }$ $A ^ { \prime }$

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Definitions:

Slope

The measure of the steepness or incline of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Dependent Variable

A variable in an experiment or model whose changes depend on the effects of other variables.

Independent Variable

A variable that is manipulated to determine its effect on a dependent variable.

Critical T Value

The threshold value in t-testing that determines whether to reject the null hypothesis, based on the desired level of significance.