# Matrices And Determinants

Evaluate the determinant, using row or column operations whenever possible to simplify your work. 2.5 Points

2)

Evaluate the determinant. Use row or column operations whenever possible to simplify your work.

D = __________

2.5 Points

3)

Find the determinant of the matrix, if it exists. 2.5 Points

4)

A nutritionist is studying the effects of the nutrients folic acid, choline, and inositol. He has three types of food available, and each type contains the following amounts of these nutrients per ounce:

Type A        Type B       Type C

Folic acid (mg)    3                 1                  3

Choline (mg)      4                 2                  4

Inositol (mg)      3                 2                  4

Suppose food type C has been improperly labeled, and it actually contains 4 mg of folic acid, 6 mg of choline, and 5 mg of inositol per ounce. Would it still be possible to use matrix inversion to find the combination of foods giving the required supply.

2.5 Points

5)

Evaluate the determinant, using row or column operations whenever possible to simplify your work. 2.5 Points

6)

(a) Find the determinant of the matrix. (b) Determine whether the matrix has an inverse, but don’t calculate the inverse.

2.5 Points

7)

(a) Find the determinant of the matrix. (b) Determine whether the matrix has an inverse, but don’t calculate the inverse.

2.5 Points

8)

Use a determinant to find the area of the triangle with the given vertices.

(0, 0), (6, 2), (2, 7)

Area = __________

2.5 Points

9)

Find the inverse of the matrix if it exists. 2.5 Points

10)

Find the determinant of the matrix. 2.5 Points

11)

Solve for x.​ x = __________

2.5 Points

12)

Find the inverse of the matrix if it exists.​ 2.5 Points

· no solution

13)

Solve the system of equations by converting to a matrix equation and using the inverse of the coefficient matrix. Use the inverse of matrix.​ ​​

(x, y) = ( __________, __________ )

2.5 Points

14)

Use Cramer’s Rule to solve the system.​ 2.5 Points

15)

Use Cramer’s Rule to solve the system.​ 2.5 Points

16)

Find the determinant of the matrix, if it exists.​ Basic features
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