WEBVTT

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Here is the problem: [[1, 2, 0, 1], [0, 1, 3, 2], [2, 0, 1, 1], [1, 1, 1, 1]].

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Find the determinant of a 4 times 4 matrix.

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Read the 4 times 4 matrix.

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Reduce to upper-triangular form with row operations.

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Eliminate below the pivot in column 1 (adding row multiples keeps the determinant).

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Eliminate below the pivot in column 2 (adding row multiples keeps the determinant).

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Eliminate below the pivot in column 3 (adding row multiples keeps the determinant).

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Multiply the diagonal of the triangular matrix.

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So the answer is det(A) equals negative 2.

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The determinant is negative 2, which is non-zero, so the matrix is invertible and its rows are linearly independent.

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Computed exactly with fractions; row reduction gives the same value negative 2.