# Monthly Archives: June 2010

## Linear Algebra and Its Applications, exercise 1.4.11

Exercise 1.4.11. State whether the following statements are true or false. If a given statement is false, provide a counterexample to the statement. For two matrices A and B, if the first column of B is identical to the third … Continue reading

## Linear Algebra and Its Applications, exercise 1.4.10

Exercise 1.4.10. Given a matrix A with entries , what are the following entries? first pivot the multiplier that is used to multiply the first row and subtract it from the ith row the value that replaces once the above … Continue reading

## Linear Algebra and Its Applications, exercise 1.4.9

Exercise 1.4.9. Given the following two examples of FORTRAN code DO 10 I=1,N DO 10 J=1,N 10 B(I) = B(I) + A(I,J)*X(J) and DO 10 J=1,N DO 10 I=1,N 10 B(I) = B(I) + A(I,J)*X(J) Do they multiply Ax by … Continue reading

## Linear Algebra and Its Applications, exercise 1.4.8

Exercise 1.4.8. Give non-zero examples of 3×3 matrices with the following properties: diagonal matrix ( if ); symmetric matrix ( for all ); upper triangular matrix ( if ); skew-symmetric matrix ( for all i and j). Answer: Diagonal matrix: … Continue reading

## Linear Algebra and Its Applications, exercise 1.4.7

Exercise 1.4.7. Given the n-dimensional row vector y and column vector x, express their inner product in summation notation. Answer: We have NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear … Continue reading