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Find the determinant of the matrix. [[0,7],[1,0]]

Find the determinant of the matrix.\newline[0amp;71amp;0] \left[\begin{array}{ll} 0 & 7 \\ 1 & 0 \end{array}\right]

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Full solution

Q. Find the determinant of the matrix.\newline[0710] \left[\begin{array}{ll} 0 & 7 \\ 1 & 0 \end{array}\right]
  1. Write Matrix Determinant: Write down the matrix to find its determinant.\newlineThe matrix is:\newline[0amp;7 1amp;0]\begin{bmatrix} 0 & 7 \ 1 & 0 \end{bmatrix}
  2. Use Determinant Formula: Use the formula for the determinant of a 2×22 \times 2 matrix.\newlineThe determinant of a 2×22 \times 2 matrix [aamp;b camp;d]\left[\begin{array}{cc}a & b \ c & d\end{array}\right] is ad−bcad - bc.\newlineFor our matrix, a=0a=0, b=7b=7, c=1c=1, and d=0d=0.
  3. Calculate Determinant: Calculate the determinant using the values from the matrix.\newlineDeterminant = (0×0)−(7×1)(0 \times 0) - (7 \times 1)\newlineDeterminant = 0−70 - 7\newlineDeterminant = −7-7

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