Type a math problem
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Calculate Determinant
-7
Steps Using Diagonal Rule
\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix}
Find the determinant of the matrix.
Find the determinant of the matrix.
det(\left(\begin{matrix}2&3\\5&4\end{matrix}\right))
For the 2\times 2 matrix \left(\begin{matrix}a&b\\c&d\end{matrix}\right), the determinant is ad-bc.
For the matrix , the determinant is .
2\times 4-3\times 5=-7
Multiply 2 times 4.
Multiply times .
8-3\times 5=-7
Multiply 3 times 5.
Multiply times .
8-15=-7
Subtract 15 from 8.
Subtract from .
-7
Evaluate
\left(\begin{matrix}2&3\\5&4\end{matrix}\right)
Invert Matrix
\left(\begin{matrix}-\frac{4}{7}&\frac{3}{7}\\\frac{5}{7}&-\frac{2}{7}\end{matrix}\right)
Calculate Trace
6
Transpose Matrix
\left(\begin{matrix}2&5\\3&4\end{matrix}\right)
Matrix Size
2,2
Reduce Matrix
\left(\begin{matrix}1&0\\0&1\end{matrix}\right)
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det(\left(\begin{matrix}2&3\\5&4\end{matrix}\right))
Find the determinant of the matrix.
2\times 4-3\times 5=-7
For the 2\times 2 matrix \left(\begin{matrix}a&b\\c&d\end{matrix}\right), the determinant is ad-bc.
8-3\times 5=-7
Multiply 2 times 4.
8-15=-7
Multiply 3 times 5.
-7
Subtract 15 from 8.
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