1. If A and B are different rank-one matrices ( A* B), then the rank of A-B is a =2 b. d 21 c. If the complete solution of Ax= is x= then o -1./ 0 -2 1 2 A = 1' 0 (d. A= 2 0 b. A = C. -1 -2 Let the first two columns of a matrix A be Then, the dimension of the row space of and A is Larger than or equal to 2 b. Larger than or equal to 1 C. Equal to 2 d. Equal to 1 Only one of the following can be the null space matrix of a full row rank 2×3 matrix [1 1 1 0 0 3.13-2) 13x1) 0. a. b. с. Let A be a 3x3 matrix. Assume the sums of the elements in each column and the sums of the ulements in each row of A are zeros. Then, the vector g =[c c c',where c is an arbitrary non- constant scalar, belongs to both olumn space ofo. The null space of A and the row space of A c. The null space of A and the row space of A d. The column space and the left null space of A of A and the left null space of A Consider the plane defined by x, +2x2 - 3x3 =0. The basis vectors of this plane are -2][3 C. d. 1 Given that x, and x, are the particular solution and the null space solution of Ax=b , and that c i an arbitrary constant, then the complete solution has the general form: a. . c(x, + Xn) b.. cxp+ Xn Xp+cx, d. Xp+ Xn hich of the following sets of vectors can be basis of R a. b. с. Let A be an m xn matrix of rank r. Let Ax=b have solutions for all possible choices of b. One o: the following expressions must be true: a. r=m-n =n- m C. m2n H nzm
1. If A and B are different rank-one matrices ( A* B), then the rank of A-B is a =2 b. d 21 c. If the complete solution of Ax= is x= then o -1./ 0 -2 1 2 A = 1' 0 (d. A= 2 0 b. A = C. -1 -2 Let the first two columns of a matrix A be Then, the dimension of the row space of and A is Larger than or equal to 2 b. Larger than or equal to 1 C. Equal to 2 d. Equal to 1 Only one of the following can be the null space matrix of a full row rank 2×3 matrix [1 1 1 0 0 3.13-2) 13x1) 0. a. b. с. Let A be a 3x3 matrix. Assume the sums of the elements in each column and the sums of the ulements in each row of A are zeros. Then, the vector g =[c c c',where c is an arbitrary non- constant scalar, belongs to both olumn space ofo. The null space of A and the row space of A c. The null space of A and the row space of A d. The column space and the left null space of A of A and the left null space of A Consider the plane defined by x, +2x2 - 3x3 =0. The basis vectors of this plane are -2][3 C. d. 1 Given that x, and x, are the particular solution and the null space solution of Ax=b , and that c i an arbitrary constant, then the complete solution has the general form: a. . c(x, + Xn) b.. cxp+ Xn Xp+cx, d. Xp+ Xn hich of the following sets of vectors can be basis of R a. b. с. Let A be an m xn matrix of rank r. Let Ax=b have solutions for all possible choices of b. One o: the following expressions must be true: a. r=m-n =n- m C. m2n H nzm
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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Transcribed Image Text:1. If 4 and B are different rank-one matrices ( A* B ), then the rank of A–B is
a.
= 2
b. =1
c.
= 0
(d. 21
If the complete solution of Ax =
is x=
then
o -1./
0 -2
|- a- O -
2
b.
A =
c.
A =
-1 -2
A =
2 0
-2 -2
1
Then, the dimension of the row space of
Let the first two columns of a matrix A be
and
A is
Larger than or equal
to 2
b. Larger than or equal
to 1
Equal to 2
d. Equal to 1
Only one of the following can be the null space matrix of a full row rank 2×3 matrix
3.13-2)
a.
b.
1 1
0 0
c.
d.
13x)
Let A be a 3x3 matrix. Assume the sums of the elements in each column and the sums of the
ulements in each row of A are zeros. Then, the vector g =[c c c,where c is an arbitrary non-
constant scalar, belongs to both
olumn space of-
and the row
The null space of A
and the left null space
c. The null space of
A and the row
space of A
d. The column space
of A and the left
null space of A
space of A
of A
Consider the plane defined by x, +2x2 - 3x3 =0. The basis vectors of this plane are
-3
d.
1
1
Given that
Xp
and
x, are the particular solution and the null space solution of Ax = b , and that c i
an arbitrary constant, then the complete solution has the general form:
a. c(xp
+ x„)
b.. cx, + Xn
Xp+cx,
d. Xp+ Xn
nich of the following sets of vectors can be basis of R?
G.
a,
b.
C.
Let A be an mxn matrix of rank r . Let Ax=b have solutions for all possible choices of b. One o!
the following expressions must be true:
a.
r=m-n
Or =n- m
C.
m2n
d nzm
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