Purchase Solution

Row Space, Column Space, and Null Space of a Matrix

Not what you're looking for?

Ask Custom Question

Let M = (1 2 1)
(0 3 2)
(-2 6 -1)
(-4 1 2)

Find the row space, the column space, and the null space of M, and give their dimensions.

Purchase this Solution

Solution Summary

We find bases for the row space, column space, and null space of a given matrix.

Solution Preview

We are given the matrix

We wish to find the row space, column space, and null space of M, and give their dimensions.

The row space of M is the vector space spanned by the rows of M. To find this vector space, we perform row reduction on M.
Adding twice the first row to the third yields
Adding ...

Purchase this Solution

Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

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

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.

Probability Quiz

Some questions on probability