Analyzing a row echelon form

Posted on by Leakey
  1. Find the row echelon form for each of the following matrices:
    2 —3 —2 (a) 2 [ 1 1 2 2 1 1 —2 —4 1 (b) 1 3 7 2 2 1 —12 —11 —16 5 0 1 3 —3 0 (c) 2 2 —6 2 0 1 4
  2. Find all solutions for the following linear systems, if any exist, by using the Gausian Elimation method:
    (a) x+y+2z=8 —x — 2y + 3z = 1 3x— 7y + 4z = 10
    (b) x + 3y — 2z + 2v = 0 2x + 6y — 5z — 2u+ 4v — 3w = —1 5z + 10u + 15w = 5 2x+6y+8u+4v+18w= 6
    (c) 3x + 2y = —12 Sr — 3y = —1 —6x — 4y = 6
    (d) 3x + 2y = —12 5x — 3y = —1 —fix — 4y = 24
  3. Solve the following linear system with the given augmented matrix: 4 —8 12 3 —6 —2 4 —6 4. Find the determinants of the following matrices:
    10 0 0 (a) 0 —7 0 0 0 6 [ 1 3 21 (b) 0 —2 1 0 0 4
    (c)
    (d)
    1 3 2 0 —2 1 1 5 1
    { 0 0 3 0 0 1 0 0 4 0 0 0 0 0 0 2
  4. Find the co-factors, adjoints, and inverses of the following matrices:
    (a) [h 12 2 2 1 0 0 (b) 0 0 1 0 1 0 1 2 3 (c) 2 5 3 1 0 8
  5. Solve the fol owing linear system using Cramer’s rule:
    2
    (a) 7x — 2y = 3 3x+y=5
    (b) x — 4y + z = 6 4x—y+2z=-1 2x + 2y — 3z = —20
  6. Find the rank of the following matrix:
    0 r0 . 0 0 —1 3 0 3 0 2 0 4 11 7
  7. Determinant properties
    (a) Show 1A-11 = (b) Consider a 3 x 3 matrix A. Add 2 x cowl to row 2 to get B. Solve for lg. (c) Let B = (aA)T where a is a constant. Derive 1B-11
  8. Find B37. Given that: B = [01 —01]

This question has been answered.

Get Answer