1.Let the null space of matrix G and the null space of matrix H_be orthogonal complements. Thenonly one of the following statement can be true:N(G) = N(H)b. N(G")=N(H") |© N()=C(H")a.d.N(G)= C(H)If the column space of a 3×3 matrix consists of all vectors b=|b2 such that b, +b2 = 3b3 thenone of the following set of vectors forms a basis for the left null space of that matrix:Vaリ(6)33b.)and3d.3с.а.and3If the vector b=|3| is projected onto the line defined by the intersection of the two planesx+ y+z =Q and x+2y+z=0, then the projection vector is equal to11d.b.a.-14The vector-1 is the orthogonal complement of the space spanned by the vectors7[2-40.14b.C.33d.'a.7C(A"), where A=2 916 5 c(AT)One of the following vectors belongs to-3b-24-2a--34-10A is an mxn matrix with rank r and the system A'y= b has exactly one solution for some b(but not for every possible b ), thenb.C.m>nd.m2nn=r

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Let the null space of matrix G and the null space of matrix H be orthogonal complements. Then only one of the following statement can be true: N(G) = N(H) 6. N(G")=N(H") N(G)=C(H") d. N(G)= C(H) %3D a. If the column space of a 3x3 matrix consists of all vectors b=|b2 | such that b, +b, = 3b, then b3 one of the following set of vectors forms a basis for the left null space of that matrix: (9)* N 3 3 (b. 3 and 3 d. 3 с. a. 1 and 3 -3 -3

Let the null space of matrix G and the null space of matrix H be orthogonal complements. Then only one of the following statement can be true: N(G) = N(H) 6. N(G")=N(H") N(G)=C(H") d. N(G)= C(H) %3D a. If the column space of a 3x3 matrix consists of all vectors b=|b2 | such that b, +b, = 3b, then b3 one of the following set of vectors forms a basis for the left null space of that matrix: (9)* N 3 3 (b. 3 and 3 d. 3 с. a. 1 and 3 -3 -3

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

1.
Let the null space of matrix G and the null space of matrix H_be orthogonal complements. Then
only one of the following statement can be true:
N(G) = N(H)
b. N(G")=N(H") |© N()=C(H")
a.
d.
N(G)= C(H)
If the column space of a 3×3 matrix consists of all vectors b=|b2 such that b, +b2 = 3b3 then
one of the following set of vectors forms a basis for the left null space of that matrix:
Vaリ(6)
3
3
b.)
and
3
d.
3
с.
а.
and
3
If the vector b=|3| is projected onto the line defined by the intersection of the two planes
x+ y+z =Q and x+2y+z=0, then the projection vector is equal to
1
1
d.
b.
a.
-1
4
The vector-1 is the orthogonal complement of the space spanned by the vectors
7
[2
-4
0.
14
b.
C.
33
d.'
a.
7
C(A"), where A=
2 9
16 5 c
(AT)
One of the following vectors belongs to
-3
b-
2
4
-2
a-
-34
-10
A is an mxn matrix with rank r and the system A'y= b has exactly one solution for some b
(but not for every possible b ), then
b.
C.
m>n
d.
m2n
n=r

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