Find the determinant of the matrix \( \begin{pmatrix} 1 & 0 & 0 \\ 0 &am
Practice Questions
Q1
Find the determinant of the matrix \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
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Questions & Step-by-Step Solutions
Find the determinant of the matrix \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
Correct Answer: 1
Step 1: Identify the matrix given in the question, which is the identity matrix: \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
Step 2: Recall the definition of the determinant. The determinant is a special number that can be calculated from a square matrix.
Step 3: Recognize that the given matrix is the identity matrix. The identity matrix is a square matrix with 1s on the diagonal and 0s elsewhere.
Step 4: Remember the property of the determinant of the identity matrix. The determinant of any identity matrix is always 1.
Step 5: Conclude that the determinant of the given matrix is 1.
Determinant of a Matrix – The determinant is a scalar value that can be computed from the elements of a square matrix and reflects certain properties of the matrix, such as whether it is invertible.
Identity Matrix – The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere, and its determinant is always 1.
