 # Systems of Linear Equations - Number of Solutions, Gauss Elimination

Subject Mathematics Linear Algebra

## Question

1. The following augmented matrices represent linear systems in three variables. In each case determine the number of solutions. You do NOT need to solve the system of equations.

2. The sum of the digits of a two-digit number is 9. When the digits are reversed, the number is decreased by 45. Find the number.

3. For the following linear system, (a) write it in augmented matrix form; (b) use Gaussian elimination to put the matrix into echelon form (EF); (c) check whether the system is consistent or inconsistent;
(d) if the system is consistent, proceed by Gauss-Jordan elimination to put the matrix into reduced row echelon form (RREF) and write down the general solution.
x₁ - x₂ + x₃ = 6
x₂ = 1
x₁ + x₃ = 2
4. Repeat the same steps (a)-(d) as in the previous question, this time for the linear system
-3x₁ + x₂ + 2x₃ = 6
4x₁ + 2x₂ - x₃ = 2
-2x₁ + 4x₂ + 3x₃ = 14

See Question.pdf

## Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

Problem 1. The system with augmented matrix A is consistent – unique solution. The ranks of both matrices:
[ 3 0 2 ]    [ 3 0 2 | 3 ]
[ 0 -2 0 ] and [ 0 -2 0 | 4 ]
[ 0 0 1 ]    [ 0 0 1 | 5 ]
are equal to 3 – the same as the number of unknowns.
The last row implies x3 = 5, 2nd row allows to determine uniquely x₂, etc....

This is only a preview of the solution. Please use the purchase button to see the entire solution

## Related Homework Solutions

Linear Algebra System of Equations, Inequalities \$8.00
System of Linear Equations
System of Linear Inequalities
Mathematics
Algebra
Linear Algebra
Linear Algebra Questions \$5.00
Linear Algebra
Mathematics
Matrix
Equation
Pivot Position
Linearly Independent Columns
True Statements
False Statements
One to One
Linear Transformations
Subspace
Vectors
Dimensions
Linear Algebra Questions \$70.00
Linear Algebra
Mathematics
Vectors
Matlab
Data Manipulation
Random Integers
Computer Science
Gramm-Schmidt
Algorithms
Objects
Digits
Images
Linear Algebra Problem \$30.00
Linear Algebra
Matrix
Determinant
Transition Matrix
Basis
Vectors
Span
3x3 Matrix
Coordinate Vector
Bases
5 Skew Symmetric Matrix Exercises \$18.00
Skew
Symmetric
Matrix
Eigenvalues
Inner
Product
Positive
Complex
Number
Dimension
Subspace
Economic Math Problems \$30.00
Mathematics
Linear Algebra
Economics
Problems
Graph
Fixed Cost
Variable
Cost
Functions
Live Chats