# Monthly Archives: August 2010

## Linear Algebra and Its Applications, exercise 1.4.14

Exercise 1.4.14. Show example 2×2 matrices having the following properties: A matrix A with real entries such that A nonzero matrix B such that Two matrices C and D with nonzero product such that CD = -DC Two matrices E … Continue reading

Posted in linear algebra | Leave a comment

## Linear Algebra and Its Applications, exercise 1.4.13

Exercise 1.4.13. Provide an example of multiplying two 3×3 triangular matrices, to confirm the general case that the product of triangular matrices is itself a triangular matrix. Prove the general case based on the definition of matrix multiplication. Answer: An … Continue reading

Posted in linear algebra | Leave a comment

## Linear Algebra and Its Applications, exercise 1.4.12

Exercise 1.4.12. Given the matrices A and B below, the first row of their product AB is a linear combination of all the rows of B. Find the coefficients of this linear combination, and the first row of B. Answer: … Continue reading

Posted in linear algebra | Leave a comment