jee-main 2024 Q84

jee-main · India · session1_27jan_shift1 Matrices Linear System and Inverse Existence

Let $\mathrm { A } = \left[ \begin{array} { l l l } 2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \end{array} \right] , \mathrm { B } = \left[ \begin{array} { l l l } \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } & \mathrm {~B} _ { 3 } \end{array} \right]$, where $\mathrm { B } _ { 1 } , \mathrm {~B} _ { 2 } , \mathrm {~B} _ { 3 }$ are column matrices, and $\mathrm { AB } _ { 1 } = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$, $\mathrm { AB } _ { 2 } = \left[ \begin{array} { l } 2 \\ 3 \\ 0 \end{array} \right] , \mathrm { AB } _ { 3 } = \left[ \begin{array} { l } 3 \\ 2 \\ 1 \end{array} \right]$ If $\alpha = | \mathrm { B } |$ and $\beta$ is the sum of all the diagonal elements of B, then $\alpha ^ { 3 } + \beta ^ { 3 }$ is equal to

Let $\mathrm { A } = \left[ \begin{array} { l l l } 2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \end{array} \right] , \mathrm { B } = \left[ \begin{array} { l l l } \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } & \mathrm {~B} _ { 3 } \end{array} \right]$, where $\mathrm { B } _ { 1 } , \mathrm {~B} _ { 2 } , \mathrm {~B} _ { 3 }$ are column matrices, and $\mathrm { AB } _ { 1 } = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$, $\mathrm { AB } _ { 2 } = \left[ \begin{array} { l } 2 \\ 3 \\ 0 \end{array} \right] , \mathrm { AB } _ { 3 } = \left[ \begin{array} { l } 3 \\ 2 \\ 1 \end{array} \right]$\\
If $\alpha = | \mathrm { B } |$ and $\beta$ is the sum of all the diagonal elements of B, then $\alpha ^ { 3 } + \beta ^ { 3 }$ is equal to

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