If \( I = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), what is \( |I

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Question: If \\( I = \\begin{pmatrix} 1 & 1 \\\\ 1 & 1 \\end{pmatrix} \\), what is \\( |I| \\)? (2021)

Options:

Correct Answer: 0

Exam Year: 2021

Solution:

The determinant is \\( 1*1 - 1*1 = 1 - 1 = 0 \\).

If \( I = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), what is \( |I| \)? (2021)

If \( I = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), what is \( |I| \)? (2021)

Step 1: Identify the matrix I, which is given as I = [[1, 1], [1, 1]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is |A| = ad - bc, where A = [[a, b], [c, d]].
Step 3: In our matrix I, a = 1, b = 1, c = 1, and d = 1.
Step 4: Substitute the values into the determinant formula: |I| = (1 * 1) - (1 * 1).
Step 5: Calculate the multiplication: 1 * 1 = 1 and 1 * 1 = 1.
Step 6: Now, subtract the second result from the first: 1 - 1 = 0.
Step 7: Conclude that the determinant |I| 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.