Haynes Spencer
05/20/2024 · Junior High School
Determinante de B \( \mathrm{B}=\left[\begin{array}{lll}3 & 2 & 1 \\ 4 & 0 & 1 \\ 0 & 1 & 1\end{array}\right] \)
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Calculate the determinant of the matrix \( \begin{bmatrix} 3 & 2 & 1 \\ 4 & 0 & 1 \\ 0 & 1 & 1 \end{bmatrix} \).
Matrices by following steps:
- step0: Evaluate the determinant:
\(\left[\begin{array}{rrr}{3}&{2}&{1}\\{4}&{0}&{1}\\{0}&{1}&{1}\end{array}\right]\)
- step1: Use the appropriate notation:
\(\left|\begin{array}{cc}{3}&{2}&{1}\\{4}&{0}&{1}\\{0}&{1}&{1}\end{array}\right|\)
- step2: Use cofactor expansion along a row:
\(-4\times \left|\begin{array}{cc}{2}&{1}\\{1}&{1}\end{array}\right|+0\times \left|\begin{array}{cc}{3}&{1}\\{0}&{1}\end{array}\right|-1\times \left|\begin{array}{cc}{3}&{2}\\{0}&{1}\end{array}\right|\)
- step3: Evaluate the determinant:
\(-4\times 1+0-1\times 3\)
- step4: Evaluate:
\(-4+0-3\)
- step5: Remove 0:
\(-4-3\)
- step6: Subtract the numbers:
\(-7\)
El determinante de la matriz \( B \) es -7.
Quick Answer
El determinante de la matriz \( B \) es -7.
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