Math Problem Statement

Solve 14 and 15

Solve problems 14 and 15 from the provided image using augmented matrices.

Solution

Let's solve the systems of equations given in problems 14 and 15 using augmented matrices.


Problem 14:

The system is: 2x+6y+8z=52x + 6y + 8z = 5 2x+9y12z=1-2x + 9y - 12z = -1 4x+6y4z=34x + 6y - 4z = 3

The augmented matrix is:

2 & 6 & 8 & | & 5 \\ -2 & 9 & -12 & | & -1 \\ 4 & 6 & -4 & | & 3 \end{bmatrix}$$ --- ### Problem 15: The system is

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Systems of Linear Equations
Matrix Operations

Formulas

Row operations in augmented matrices
Gaussian elimination method

Theorems

Consistency of linear systems
Properties of augmented matrices

Suitable Grade Level

Grades 10-12