If C = [[1, 0, 0], [0, 1, 0], [0, 0, 0]], what is the determinant of C? (2022)
Practice Questions
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If C = [[1, 0, 0], [0, 1, 0], [0, 0, 0]], what is the determinant of C? (2022)
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Questions & Step-by-Step Solutions
If C = [[1, 0, 0], [0, 1, 0], [0, 0, 0]], what is the determinant of C? (2022)
Step 1: Identify the matrix C, which is given as C = [[1, 0, 0], [0, 1, 0], [0, 0, 0]].
Step 2: Look at the rows of the matrix. The third row is [0, 0, 0], which means it is a row of zeros.
Step 3: Recall the property of determinants: if a matrix has a row (or column) of zeros, its determinant is 0.
Step 4: Since matrix C has a row of zeros, we conclude that the determinant of C is 0.
Determinant of a Matrix – The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties about the matrix, such as whether it is invertible.
Properties of Determinants – One key property is that if a matrix has a row or column of zeros, its determinant is zero.
