21.3.5. Determinants

Try these first

1. 1.

   Calculate the determinant of the matrix [[2, 3], [1, 4]].

   Hint

   Use the formula: ad - bc for a 2x2 matrix.

2. 2.

   Is the matrix [[0, 0], [0, 0]] singular or non-singular?

   Hint

   Check if the determinant is zero.

3. 3.

   What is the determinant of a matrix A = [[1, 2], [3, 4]]?

   • -2
   • 0
   • 2

   Hint

   Use the formula for a 2x2 matrix.

4. 4.

   True or False: If det(A) = 0, then A is invertible.

   • True
   • False

   Hint

   Think about the meaning of a singular matrix.

5. 5.

   Given a 3x3 matrix A where A = [[2, -1, 3], [1, 0, 4], [0, 1, 5]], compute the determinant and interpret its significance.

   Hint

   Use the cofactor expansion method for 3x3 matrices.

6. 6.

   Consider two matrices A and B where det(A) = 6 and det(B) = 2. What is the determinant of the inverse of matrix A and the product of A and B?

   Hint

   Review properties of determinants for inverses and products.