Consider the Difference Equation $\mathbf { x } _ { \mathbf { k } + 1 } = \mathrm { Ax } _ { \mathbf { k } }$

question 7

Multiple Choice

Consider the difference equation $\mathbf { x } _ { \mathbf { k } + 1 } = \mathrm { Ax } _ { \mathbf { k } }$ , where $\mathrm { A }$ has eigenvalues and corresponding eigenvectors $\mathbf { v } _ { 1 }$ , $\mathbf { v } _ { 2 }$ , and $\mathbf { v } _ { 3 }$ given below. Find the general solution of this difference equation if $x _ { 0 }$ is given as below.

- $\lambda _ { 1 } = 1.3 , \lambda _ { 2 } = 0.8 , \lambda _ { 3 } = 0.6 , \mathbf { v } _ { 1 } = \left[ \begin{array} { r } - 6 \\ 6 \\ 1 \end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { l } 2 \\ 1 \\ 2 \end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r } 1 \\ 2 \\ - 2 \end{array} \right]$ , and $\mathbf { x } _ { 0 } = \left[ \begin{array} { r } - 33 \\ 33 \\ - 7 \end{array} \right]$

• A)
• \(\mathrm{x}_{\mathrm{k}}=(1.3)^{\mathrm{k}_{\mathbf{v1}}}-3(0.8)^{\mathrm{k}_{\mathbf{}}} \mathbf{v}_{2}+3(0.6)^{\mathrm{k}_{\mathbf{v3}}}\)
• B)
• \(\mathrm{x}_{\mathrm{k}}=(1.3)^{\mathrm{k}_{\mathbf{v1}}}+(0.8)^{\mathrm{k}_{\mathbf{v2}}}+(0.6)^{\mathrm{k}_{\mathbf{v3}}}\)
• C) \(\mathbf { x } _ { \mathrm { k } } = 5 ( 1.3 ) ^ { \mathrm { k } _ { \mathbf { v1 } } } - 3 ( 0.8 ) ^ { \mathrm { k } _ { \mathbf {v2} } } + ( 0.6 ) ^ { \mathrm { k } _ { \mathbf { v3 } } }\)
• D) \(\mathbf { x } _ { \mathrm { k } } = 5 ( 1.3 ) ^ { \mathrm { k } _ { \mathbf { v1 } } } - 3 ( 0.8 ) ^ { \mathrm { k } _ { \mathbf { v2 } } } + 3 ( 0.6 ) ^ { \mathrm { k } _ { \mathbf { v3 } } }\)

Recognize the impact of individual beliefs on attitudes and behaviors.

Comprehend the criticisms and limitations of need achievement theory and other personality and motivation assessments.

Examine the factors contributing to the approach or avoidance of achievement situations.

Understand the concepts of structural isomerism and conformational isomerism in organic compounds.

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