# Tag Archives: orthogonal subspaces

## 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

Posted in linear algebra | | 6 Comments

## Linear Algebra and Its Applications, Exercise 3.1.20

Exercise 3.1.20. Suppose is a subspace of . Show that . What does this mean? Answer: We first consider the case where ; in other words, contains only the zero vector. From exercise 3.1.18 we know that . The only … Continue reading

Posted in linear algebra | | 1 Comment

## Linear Algebra and Its Applications, Exercise 3.1.19

Exercise 3.1.19. State whether each of the following is true or false: (a) If the subspaces and are orthogonal, then and are also orthogonal. (b) If is orthogonal to and orthogonal to then is orthogonal to . Answer: (a) In … Continue reading