Linear Algebra and Its Applications, Review Exercise 2.12

Posted on November 10, 2013 by hecker

Review exercise 2.12. The matrix $A$ is $n$ by $n-1$ and has rank $n-2$ . What is the dimension of its nullspace?

Answer: The dimension of the nullspace $\mathcal{N}(A)$ is the number of columns of $A$ minus the rank of $A$ , or $(n-1) - (n-2) = 1$ .

NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.

If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books.

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