Find the value of \( \det \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
Practice Questions
1 question
Q1
Find the value of \( \det \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
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The determinant of the identity matrix is always 1.
Questions & Step-by-step Solutions
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Q
Q: Find the value of \( \det \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
Solution: The determinant of the identity matrix is always 1.
Steps: 4
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.
