
Archives
 January 2021
 March 2019
 January 2018
 December 2017
 January 2017
 December 2016
 November 2016
 October 2016
 September 2016
 July 2016
 October 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
 September 2011
 August 2011
 July 2011
 June 2011
 May 2011
 April 2011
 March 2011
 January 2011
 August 2010
 June 2010
 May 2010
 November 2009

Meta
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
Posted in linear algebra
Leave a comment
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
Posted in linear algebra
Leave a comment
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
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, exercise 1.4.8
Exercise 1.4.8. Give nonzero examples of 3×3 matrices with the following properties: diagonal matrix ( if ); symmetric matrix ( for all ); upper triangular matrix ( if ); skewsymmetric matrix ( for all i and j). Answer: Diagonal matrix: … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, exercise 1.4.7
Exercise 1.4.7. Given the ndimensional 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
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, exercise 1.4.6
Exercise 1.4.6. Find the 3×2 matrix A for which . Find the 3×2 matrix B for which . Answer: We have We also have NOTE: This continues a series of posts containing worked out exercises from the (out of print) … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, exercise 1.4.5
Exercise 1.4.5. Multiply the following matrices: Considering the matrix A as a system of equations, find a solution to the system Ax = 0, for which the righthand side of all three equations is zero. Specify whether there is just … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, exercise 1.4.4
Exercise 1.4.4. Compute the number of multiplications required to multiply an mxn matrix A by an ndimensional vector x. Also compute the number of multiplications required to multiply A by an nxp matrix B. Answer: The result of multiplying A … Continue reading
Posted in linear algebra
1 Comment
Linear Algebra and Its Applications, exercise 1.4.3
Exercise 1.4.3. Multiply the matrices below: Answer: The first example multiplies a 1×3 matrix by a 3×1 matrix producing a 1×1 matrix, i.e., a scalar value: As noted in the book, the result is equal to the square of the … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, exercise 1.4.2
Exercise 1.4.2. Multiply the matrices below: Work by columns instead of by rows. Answer: The first example multiplies a 3×2 matrix by a 2×1 matrix (column vector), producing a 3×1 matrix (column vector). Working by rows gives us the following: … Continue reading
Posted in linear algebra
Leave a comment