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What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 &

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Question: What is the determinant of the matrix \\( A = \\begin{pmatrix} 1 & 2 \\\\ 3 & 4 \\end{pmatrix} \\)? (2021)

Options:

  1. -2
  2. 2
  3. 0
  4. 4

Correct Answer: -2

Solution: 

The determinant of a 2x2 matrix \\( A = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix} \\) is given by \\( ad - bc \\). Here, \\( 1*4 - 2*3 = 4 - 6 = -2 \\).

What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 &

Practice Questions

Q1
What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)? (2021)
  1. -2
  2. 2
  3. 0
  4. 4

Questions & Step-by-Step Solutions

What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)? (2021)
  • Step 1: Identify the elements of the matrix A. The matrix A is given as A = [[1, 2], [3, 4]]. Here, a = 1, b = 2, c = 3, and d = 4.
  • Step 2: Use the formula for the determinant of a 2x2 matrix, which is det(A) = ad - bc.
  • Step 3: Substitute the values into the formula. Calculate a * d = 1 * 4 = 4.
  • Step 4: Calculate b * c = 2 * 3 = 6.
  • Step 5: Now, subtract the second result from the first: 4 - 6 = -2.
  • Step 6: The determinant of the matrix A is -2.
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