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Given the Following Matrices Show That (A+B)=A+B( \boldsymbol { A } + \boldsymbol { B } ) ^ { \prime } = \boldsymbol { A } ^ { \prime } + \boldsymbol { B } ^ { \prime }

question 9

Essay

Given the following matrices A=(a11a12a21a22),B=(b11b12b21b22), and C=(c11c12c13c21c22c23)\boldsymbol { A } = \left( \begin{array} { l l } a _ { 11 } & a _ { 12 } \\a _ { 21 } & a _ { 22 }\end{array} \right) , \boldsymbol { B } = \left( \begin{array} { l l } b _ { 11 } & b _ { 12 } \\b _ { 21 } & b _ { 22 }\end{array} \right) , \text { and } \boldsymbol { 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)=A+B( \boldsymbol { A } + \boldsymbol { B } ) ^ { \prime } = \boldsymbol { A } ^ { \prime } + \boldsymbol { B } ^ { \prime } and (AC)=CA( \boldsymbol { A } \boldsymbol { C } ) ^ { \prime } = \boldsymbol { C } ^ { \prime } \boldsymbol { A } ^ { \prime } .

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Dispositional Characteristics

Traits or aspects of an individual's personality that are inherent and influence behavior in various situations.

Conscientiousness

A personality trait characterized by thoroughness, diligence, and reliability; an important aspect influencing job performance and personal success.

Big Five

A personality model describing five major dimensions of human personality: openness, conscientiousness, extraversion, agreeableness, and neuroticism.

Concurrent Validity

The extent to which test scores (or other predictor information) match criterion obtained at about the same time from current employees

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