Murray Reeves
06/29/2023 · High School
The value of the determinant \( \left|\begin{array}{rrr}3 & -1 & 4 \\ 6 & 3 & 5 \\ 2 & -1 & 6\end{array}\right| \)
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Calculate or simplify the expression \( \left|\begin{array}{rrr}3 & -1 & 4 \\ 6 & 3 & 5 \\ 2 & -1 & 6\end{array}\right| \).
Matrices by following steps:
- step0: Solution:
\(\left|\begin{array}{cc}{3}&{-1}&{4}\\{6}&{3}&{5}\\{2}&{-1}&{6}\end{array}\right|\)
- step1: Use cofactor expansion along a row:
\(3\times \left|\begin{array}{cc}{3}&{5}\\{-1}&{6}\end{array}\right|-\left(-\left|\begin{array}{cc}{6}&{5}\\{2}&{6}\end{array}\right|\right)+4\times \left|\begin{array}{cc}{6}&{3}\\{2}&{-1}\end{array}\right|\)
- step2: Evaluate the determinant:
\(3\times 23-\left(-26\right)+4\left(-12\right)\)
- step3: Evaluate:
\(69-\left(-26\right)-48\)
- step4: Rewrite the expression:
\(69+26-48\)
- step5: Calculate:
\(47\)
The value of the determinant \( \left|\begin{array}{rrr}3 & -1 & 4 \\ 6 & 3 & 5 \\ 2 & -1 & 6\end{array}\right| \) is 47.
Quick Answer
El valor del determinante \( \left|\begin{array}{rrr}3 & -1 & 4 \\ 6 & 3 & 5 \\ 2 & -1 & 6\end{array}\right| \) es 47.
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