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If \( E = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), what is \( |E
If \( E = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), what is \( |E| \)? (2022)
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If \( E = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), what is \( |E| \)? (2022)
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The determinant is \( 1*1 - 1*1 = 1 - 1 = 0 \).
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Q: If \( E = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), what is \( |E| \)? (2022)
Solution:
The determinant is \( 1*1 - 1*1 = 1 - 1 = 0 \).
Steps: 7
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Step 1: Identify the matrix E, which is given as E = [[1, 1], [1, 1]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is |A| = a*d - b*c, where A = [[a, b], [c, d]].
Step 3: In our matrix E, we have a = 1, b = 1, c = 1, and d = 1.
Step 4: Substitute the values into the determinant formula: |E| = 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 |E| is 0.
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