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Matrices and Linear Algebra: If (P = begin

If (P = begin{vmatrix} 1 & 1 \ 2 & 1 end{vmatrix}), find ((P^{2} + P)).

  • A.
    (begin{vmatrix} 4 & 3 \ 6 & 1 end{vmatrix})
  • B.
    (begin{vmatrix} 4 & 3 \ 6 & 4 end{vmatrix})
  • C.
    (begin{vmatrix} 2 & 2 \ 6 & 2 end{vmatrix})
  • D.
    (begin{vmatrix} 3 & 2 \ 6 & 4 end{vmatrix})
Correct Answer: Option B
Explanation

( P^{2} = begin{vmatrix} 1 & 1 \ 2 & 1 end{vmatrix} begin{vmatrix} 1 & 1 \ 2 & 1 end{vmatrix})

(begin{vmatrix} 1 times 1 + 1 times 2 & 1 times 1 + 1 times 1 \ 2 times 1 + 1 times 2 & 2 times 1 + 1 times 1 end{vmatrix})

= (begin{vmatrix} 3 & 2 \ 4 & 3 end{vmatrix} + begin{vmatrix} 1 & 1 \ 2 & 1 end{vmatrix})

= (begin{vmatrix} 4 & 3 \ 6 & 4 end{vmatrix})