# Tag Archives: left nullspace

## Linear Algebra and Its Applications, Exercise 3.3.14

Exercise 3.3.14. Find the projection matrix onto the plane spanned by the vectors and . Find a nonzero vector that projects to zero. Answer: The plane in question is the column space of the matrix The projection matrix . We have … Continue reading

## Linear Algebra and Its Applications, Exercise 3.3.12

Exercise 3.3.12. Given the subspace spanned by the two vectors and find the following: a) a set of basis vectors for b) the matrix that projects onto c) the vector in that has the minimum distance to the vector in Answer: … Continue reading

## Linear Algebra and Its Applications, Exercise 3.3.6

Exercise 3.3.6. Given the matrix and vector defined as follows find the projection of onto the column space of . Decompose the vector into the sum of two orthogonal vectors and where is in the column space. Which subspace is in? … Continue reading

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## Linear Algebra and Its Applications, Exercise 3.1.13

Exercise 3.1.13. Provide a picture showing the action of in sending the column space of to the row space and the left nullspace to zero. Answer: I’m leaving this post as a placeholder until I have time to illustrate this. … Continue reading