8. Let L: R5 → R' be the linear transfor mation defined by 1 0 1 0 2 0 -1 0 0 -1 -1 3 -1 2 -1 -1 1 (a) Find the basis and the dimension of ker L. (b) Find the basis and the dimension of range L

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 47EQ
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Please solve Q 8

6.
(a) Find the equations of the plane containing the points P(1, 3, 7), R(0, -1, –2) and S(-2, – 4, –3).
(b) Find the equations of the line containing the points (-3, 5, 4) and perpendicular to the plane 2r – 3y + 4z = 5.
7. Find a basis and dimension for the su bspace V = smns of R' where S = {r,#2, F3, X 4} and
2
2
3
,24 =
3
1
8. Let L: RS → R' be the linear transfor mation defined by
1
-1
3
-1
32
1 0
0 2
-1
L.
I3
2 0
-1
-1
0 0
-1
1
(a) Find the basis and the dimension of ker L.
(b) Find the basis and the dimension of range L
Transcribed Image Text:6. (a) Find the equations of the plane containing the points P(1, 3, 7), R(0, -1, –2) and S(-2, – 4, –3). (b) Find the equations of the line containing the points (-3, 5, 4) and perpendicular to the plane 2r – 3y + 4z = 5. 7. Find a basis and dimension for the su bspace V = smns of R' where S = {r,#2, F3, X 4} and 2 2 3 ,24 = 3 1 8. Let L: RS → R' be the linear transfor mation defined by 1 -1 3 -1 32 1 0 0 2 -1 L. I3 2 0 -1 -1 0 0 -1 1 (a) Find the basis and the dimension of ker L. (b) Find the basis and the dimension of range L
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