FINDING DETERMINANT OF A SQUARE MATRIX

Evaluate the following determinants.

Problem 1 :

Solution:

Problem 2 :

Solution:

Problem 3 :

Solution:

Problem 4 :

Solution:

Evaluate each determinant.

Problem 5 :

Solution:

Problem 6 :

Solution:

Find the area of a triangle with the given vertices.

Problem 7 :

(-2, 5), (6, 3) and (0, -8)

Solution:

To find the area of the triangle by joining the point given in the formula,

Substitute the given values in the above formula, we get

Since the area of the triangle cannot be negative, the value of k = 50 square units.

Problem 8 :

(2, 5.5), (-3.5, 12) and (-5, -1.5)

Solution:

To find the area of the triangle by joining the point given in the formula,

Substitute the given values in the above formula, we get