What is the determinant of the matrix \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)?
Practice Questions
1 question
Q1
What is the determinant of the matrix \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)?
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The determinant of the identity matrix is 1.
Questions & Step-by-step Solutions
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Q
Q: What is the determinant of the matrix \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)?
Solution: The determinant of the identity matrix is 1.
Steps: 4
Step 1: Identify the matrix given in the question. It is a 3x3 matrix: \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
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 is a special number that can be calculated from a matrix. For the identity matrix, the determinant is always 1.
Step 4: Conclude that the determinant of the given matrix is 1.
