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Linear Algebra Problems

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I have two questions that I need help with.
1) How would you find a basis of the kernel, a basis of the image and determine the dimension of each for this matrix? The
matrix is in the attachment.
2) Are the following 3 vectors linearly dependent? (see attachment for the three vectors) How can you decide?

I hope you can help me. Thanks.

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Solution Summary

This response provides the solutions for the two linear algebra problems.

Solution Preview

Linear Algebra questions are indeed tricky. I have attached the solutions (see attachment) (also below, but see the attached file has the best formatting). I hope this helps in your understanding of these types of linear algebraic problems.


Problem 1:

The kernel is the vector subspace that maps into the zero vector. It
represents the number of dimensions lost in the transformation. So:

Dimension of range = dimension of domain - dimension of kernel

The rank ...

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