# Monthly Archives: August 2010

## Linear Algebra and Its Applications, exercise 1.4.24

Exercise 1.4.24. The following matrices can be multiplied using block multiplication, with the indicated submatrices within the matrices multiplied together: Provide example matrices matching the templates above and use block multiplication to multiply them together. Provide two example templates for … Continue reading

## Linear Algebra and Its Applications, exercise 1.4.23

Exercise 1.4.23. Find the results of squaring, cubing, and in general raising to the power of n the following matrices: Answer: For the matrix A we have By induction we have for all n. For the matrix B we have … Continue reading

## Linear Algebra and Its Applications, exercise 1.4.22

Exercise 1.4.22. The x-y plane can be rotated through an angle by the following matrix: Show that . Hint: use the identities for and . Compute . Answer: (a) We have We can simplify the final matrix using the following … Continue reading

## Linear Algebra and Its Applications, exercise 1.4.21

Exercise 1.4.21. An alternative way to compute the matrix product AB is as the sum where is the ith column of A, is the ith row of B, and the product is a matrix. Provide an example showing the procedure … Continue reading

## Linear Algebra and Its Applications, exercise 1.4.20

Exercise 1.4.20. If A and B are two nxn matrices with all entries equal to 1, what are the entries of their product AB? Use the following summation formula to find the answer: Also, if C is a third nxn … Continue reading