Exercises and Problems in Linear Algebra

EXERCISES OF MATRICES OPERATIONS 3 (24) If A,Bare both n×nmatrices and ABis singular, then Ais singular or Bis singular (25) Ais diagonalizable, then Ais non-singular (26) Ais symmetric, then Ais non-singular (27) If all the eigenvalues of Aare 1, then Ais similar to the identity matrix (28) If all the eigenvalues of Aare 1, then Ais non

Exercises with Matrices

In this part, think of x, y, and X as matrices containing economic data The sample mean or average of n numbers is n i i1 1 x n = = ∑x The sample variance of the numbers is a measure of how much they vary: 2 n 2 x i i1 1 (x x) n1= σ= − − ∑ The sample covariance

EXERCISE 1 - WordPresscom

Feb 03, 2018 · MATRICES AND DETERMINANTS CLASS 12 EXERCISE 1 Q1 (i) If a matrix has 5 elements, write all possible orders it can have? (ii) If a matrix has 8 elements, write all possible orders it can have? Q2 (i) For a 2 × 2 matrix, A = [ ], whose elements are given by by = , write the value of 12

Exercise Set 1 - Colorado State University

In Exercise 27–Exercise 28, find all values of c, if any, for which the given matrix is invertible 27 Answer: 28 In Exercises 29–32, write the given matrix as a product of elementary matrices 29 Answer: 30 31 Answer:

9 1803 Linear Algebra Exercises

9C-2 Compute the determinants of the following matrices, and if the determinant is nonzero nd the inverse (a) 1 a 0 1 (b) 2 4 1 a b 0 1 c 0 0 1 3 5 (c) 2 4 0 1 1 1 0 1 1 1 0 3 5 (d) 2 6 6 4 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 3 7 7 5 9D Eigenvalues and Eigenvectors 9D-1 (a) Find the eigenvalues and eigenvectors of the matrices A = 1 1 0 2 and B