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