linear algebra sample final

Linear algebra is mainly use to find the solution of systems of linear equations in some unknowns. Linear algebra has a demonstration in analytic geometry and is generalize in operator theory. Linear algebra associates with the families of vectors called vector spaces, and with functions contain one input vector and output another vector, according to rules. Linear algebra has the application with the theory of systems of linear equations, determinants, and matrices. The sample problems are discussed below for final review.

Linear Algebra Sample Problems for Final:

The sample problems are solved in detail for final review as shown below.

Problem 1:

Evaluate the linear equation   -3(x - 4) / 6 - (x - 2) / 3 = -2 x

Sol:

The given equation has rational expressions. To eliminate the denominators by multiplying by the LCD
-3(x - 4) / 6 - (x - 2) / 3 = -2 x

The LCD is equal to 6*3 = 18. Multiply both sides by LCD.
18 * [-3 (x - 4) / 6 - (x - 2) / 3] = 18* [-2 x]

Simplify to eliminate the denominator.
-9(x - 4) - 6(x - 2) = -36x

Multiply factors and grouping the terms

-15x + 48 = -36x

Subtract 48 to both sides
-15x + 48 - 48 = -36x -48

Group like terms
-15x = -36x - 48

Add 36x to both sides
-13x + 36x = -36x - 48 +36x

Grouping the terms
23x = -48

Multiply both sides by `1/23 `
x = - `48/23`

Conclusion:
x = - `48/23` is the solution for the above given equation.

Sample Linear Algebra Practice Problems for Final:

1) Evaluate the linear equation   -3(x - 4) / 7 - (x - 2) / 2 = -2 x

2) Solve the linear equation -5(-x - 7) = 5x – 32.

3) Evaluate the linear equation   -3(-x +3) = x - 7

Answers:

1)   X = -38/15 is the solution for the above given equation.

2) The above equation has no solution.

3)  X=One is the solution for the above equation.