Find the value of \( \det \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0
Practice Questions
Q1
Find the value of \( \det \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
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Questions & Step-by-Step Solutions
Find the value of \( \det \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
Step 1: Identify the matrix given in the question. It is a 3x3 matrix that looks like this: \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
Step 2: Recognize that this matrix is called the identity matrix. The identity matrix has 1s on the diagonal (from the top left to the bottom right) and 0s everywhere else.
Step 3: Understand that the determinant of the identity matrix is a special case. It is always equal to 1, regardless of its size.
Step 4: Conclude that the value of the determinant for 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 provides important properties about 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.
