# Tag Archives: orthogonal vectors

## Linear Algebra and Its Applications, Exercise 3.1.7

Exercise 3.1.7. For the matrix find vectors and such that is orthogonal to the row space of and is orthogonal to the column space of > Answer: The nullspace of is orthogonal to the row space of . We can … Continue reading

## Linear Algebra and Its Applications, Exercise 3.1.6

Exercise 3.1.6. What vectors are orthogonal to and in ? From these vectors create a set of three orthonormal vectors (mutually orthogonal with unit length). Answer: If is a vector orthogonal to both and then the inner product of with … Continue reading

## Linear Algebra and Its Applications, Exercise 3.1.5

Exercise 3.1.5. Of the following vectors which are orthogonal to one another? Answer: We have the following inner products among the vectors: So and are orthogonal to but not to each other. NOTE: This continues a series of posts containing … Continue reading

## Linear Algebra and Its Applications, Exercise 3.1.4

Exercise 3.1.4. If is an invertible matrix, describe why row of and column of are orthogonal in the case . Answer: We have . The identity matrix has ones on the diagonal (i.e., when ) and zeros otherwise (when ). … Continue reading