# Determinants and Cramer's Rule : Row Operations and Effect on Determinant, Computing Determinants and Solving Systems of Equations

Not what you're looking for?

1. State the elementary row operation being performed and its effect on the determinant

Start with matrix

a b

c d

a.

c d

a b

b.

a b

kc kd

c.

a + kc b + kd

c d

2. Compute the determinant

a.

3 0 4

2 3 2

0 5 -1

b.

1 3 5

2 1 1

3 4 2

c.

3 5 -8 4

0 -2 3 -7

0 0 1 5

0 0 0 2

3. Use row reduction to convert the matrices to echelon for and then compute the determinant of each matrix

a.

1 3 0 2

-2 -5 7 4

3 5 2 1

1 1 2 -3

b.

1 -1 -3 2

0 1 5 4

-1 2 8 5

3 -1 -2 3

c.

1 3 -1 0 -2

0 2 -4 -1 -6

-2 -6 2 3 9

3 7 -3 8 -7

3 5 5 2 7

4. Use Cramer's Rule to compute solutions to the following systems of linear equations. (Show your work.)

a. 5x1 + 7x2 = 3

2x1 + 4x2 = 1

b. 4x1 + x2 = 6

5x1 + 2x2 = 7

c. 3x1 - 2x2 = 7

-5x1 + 6x2 = -5

d. 2x1 + x2 = 7

-3x1 + x3 = -8

x2 + 2x3 = -3

5. Compute the adjugate of the given matrices and use that information to find the inverse of each matrix

a.

0 -2 -1

3 0 0

-1 1 1

b.

3 5 4

1 0 1

2 1 1

c.

3 6 7

0 2 1

2 3 4

Please see the attached file for the fully formatted problems.

##### Purchase this Solution

##### Solution Summary

Determinants and Cramer's Rule, Row Operations and Effect on Determinant, Computing Determinants and Solving Systems of Equations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.