b. Find a similar result involving a column of zeros. 26. In each part, find a 6 x 6 matrix [a] that satisfies the stated condition. Make your answers as general as possible by using letters rather than specific numbers for the nonzero entries. a. a = 0 if ij b. a₁j = 0 if i>j c. a₁ = 0 if i 1

b. Find a similar result involving a column of zeros. 26. In each part, find a 6 x 6 matrix [a] that satisfies the stated condition. Make your answers as general as possible by using letters rather than specific numbers for the nonzero entries. a. a = 0 if ij b. a₁j = 0 if i>j c. a₁ = 0 if i 1

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 3AEXP

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1.3 Question 26 on paper please

25. a. Show that if A has a row of zeros and B is any matrix for
which AB is defined, then AB also has a row of zeros.
b. Find a similar result involving a column of zeros.
26. In each part, find a 6 x 6 matrix [a] that satisfies the stated
condition. Make your answers as general as possible by using
letters rather than specific numbers for the nonzero entries.
b. a₁ = 0 if i>j
dij
a. a = 0 if ij
c. a¡j = 0
if i<j
d. a₁ = 0
Aij
if |i-j> 1
In Exercises 27-28, how many 3x3 matrices A can you find for
which the equation is satisfied for all choices of x, y, and z?
[x+y
ху
27. Ay
28. Ay
x-y
1-6
=
0
N

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