8. Only one of the following matrices cannot be singular for any choice of real numbers a and ßaa 2a 0a+) 1aa.0 a+BB 28 0d.C.4a - /B a+48.22.Consider the system Ag=If, for any real scalar c, the vector x =solves thesystem, then-2a A--2 -2b. A=d.0 -2-2 010. Given that A and B are the two possible permutations of the 2x2 identity matrix, A+B is:A permutationmatrixb. An invertiblematrixa. A diagonal matrixC A symmetric matrix11. When the coefficient matrix of the system Ag =b is an nxn lower triangular matrix with ones onthe diagonal, then the product of the elimination matrices E is equal to:4. ATb.12. The system Ax = b, where A=0 1b = b2has a solution only1. Cannoi have asolution for any bhas a solution forHas a solution only,when b, = b, +2b2when beC(A")every b in R13. When a square matrix G is loft-multiplied by thea. The kth column of The kh row of tiethe identity matrixrow of its own inverse, the result is:a. The k columnof Ga. The k row of Gidentity matrix1 3 17then14. For the vector b=b, to be in the row space of the matrix A=|2 5 6a. by-4bz +1lb, =0b. by+4b2 +1 lb, = 0 [by - 4b, +136, =0 4 by+4b; -136, = 015. Which first row element of matrix A= 3 2 2 has no effect on the values nor the number e6 4 3pivots of A?Nene of them

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8. Only one of the following matrices cannot be singular for any choice of real numbers a and ß a a 2a 0 a a+ 1 a. 0 a+B B 28 0 d. B c. 4. a - B a+ 4 2. Consider the system .. eal scalar c the vector x= +C solves the

8. Only one of the following matrices cannot be singular for any choice of real numbers a and ß a a 2a 0 a a+ 1 a. 0 a+B B 28 0 d. B c. 4. a - B a+ 4 2. Consider the system .. eal scalar c the vector x= +C solves the

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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Question

8. Only one of the following matrices cannot be singular for any choice of real numbers a and ß
a
a 2a 0
a+) 1
a
a.
0 a+B
B 28 0
d.
C.
4
a - /
B a+
4
8.
2
2.
Consider the system Ag=
If, for any real scalar c, the vector x =
solves the
system, then
-2
a A-
-2 -2
b. A=
d.
0 -2
-2 0
10. Given that A and B are the two possible permutations of the 2x2 identity matrix, A+B is:
A permutation
matrix
b. An invertible
matrix
a. A diagonal matrix
C A symmetric matrix
11. When the coefficient matrix of the system Ag =b is an nxn lower triangular matrix with ones on
the diagonal, then the product of the elimination matrices E is equal to:
4. AT
b.
12. The system Ax = b, where A=0 1
b = b2
has a solution only
1. Cannoi have a
solution for any b
has a solution for
Has a solution only,
when b, = b, +2b2
when beC(A")
every b in R
13. When a square matrix G is loft-multiplied by the
a. The kth column of The kh row of tie
the identity matrix
row of its own inverse, the result is:
a. The k column
of G
a. The k row of G
identity matrix
1 3 17
then
14. For the vector b=b, to be in the row space of the matrix A=|
2 5 6
a. by-4bz +1lb, =0
b. by+4b2 +1 lb, = 0 [by - 4b, +136, =0 4 by+4b; -136, = 0
15. Which first row element of matrix A= 3 2 2 has no effect on the values nor the number e
6 4 3
pivots of A?
Nene of them

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