Purchase Solution

Matrix Rank and Consistent Systems of Equations

Not what you're looking for?

Ask Custom Question

1) The augmented matrix of a linear system has been transformed by row operations into the form below. Determine if the system is consistent.

2x - y + 7, x + 4y = -5

Purchase this Solution
Solution Summary

It is determined whether a system of equations is consistent. Consistent systems are determined.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

1) The augmented matrix ...

Purchase this Solution
Free BrainMass Quizzes
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.

Solving quadratic inequalities

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

Probability Quiz

Some questions on probability

Exponential Expressions

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

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Matrix Rank and Consistent Systems of Equations

    159801 Matrix Rank and Consistent Systems of Equations We are not using calculator so the steps need to be shown to the solution. 1) The augmented matrix of a linear system has been transformed by row operations into the form below.

  • concrete counter-example

    Answer is YES Explanation: By theorem, a system of linear equations AX = B is consistent if and only if A and the augmented matrix [AB] have the same rank. In the present problem it is given that A is a 3 X 5 matrix of rank 3.

  • Matrices and Linear Systems of Equations

    114120 Matrices and Linear Systems of Equations The augmented matrix of a linear system has been reduced by row operations to the form shown.

  • Matrices : Row Echelon Forms and Systems of Linear Eqations

    b) It is easy to see that the rank of the coefficient matrix is 2 but the rank of the augmented matrix is 3. As their ranks are NOT equal, the system is not consistent.

  • Normal Equations and Projection Matrices

    ,-4)^T a)Find two systems of homogeneous linear equations whose solution spaces are V and W, respectively.

  • Matrix Solutions to Systems of Linear Equations

    146041 Matrix Solutions to Systems of Linear Equations Matrices are the most common and effective way to solve systems of linear equations. However, not all systems of linear equations have unique solutions.

  • Vector Spaces : Rank

    However, if a nonzero x exists, then the columns of matrix A are linearly dependent and rank(A)=2. Solve the system of equations by the method of elimination.

  • Systems of Equations : Triangular Form and Matrices

    24265 Systems of Equations : Triangular Form and Matrices Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it.

  • Matrices : Finding the Rank

    To prove that other 3 columns are linearly independent, we need to solve a system of linear equations (A*x=0) and if its only solution is x=0, then the 3 columns are linearly independent and rank(A)=3.

View More Related Solutions