Question 6 Determine if the following subset is a subspace. Justify your an- swer. The set of polynomials p(t) with p(0) = 2 as a subset of P. In other words, H = {p(t) = Pp(0) = 2}. • The set of 2 x 2 matrices with only 0 along the main diagonal as a subset of M2x2. • {(1, 12, 13) Є R³: £1 + 4x2 + 2x3 = 0}. • {(x1, 12, 13) E R³: x1 + 4x2 + 2x3 = 6}. Question 7 Let H be the subset of R4 such that Ha subspace of R4? Justify your answer. x1+x2 x3 + x4 = 0 Is . 21 - x2 x3 x4 = 0 - 3 4 0 7 1 -52 -2 Question 8 Let A = find null space, column space and -1 4 0 3 -1 2 2 row space of A and identify their basis. Question 9 (True or False) If A = b has a solution then be Col(A). Question 10 (True or False) Let A be a 3×4 matrix, then the set of solutions of Ax = b must be a subspace of R4. Question 1 Let A = [2 4 1 7 3 -2 3 0 7-1 -5 4 " write down the cofactor expansion 1 2 -5 of det A with respect to the third column. You do not need to compute. a b C Question 2 Suppose d 9 - - 2a d 2b e 2c-f e f 4. Compute d-5g e-5h f-5i -3g -3h -3i h i Question 3 (True or False) Let A, B be two nxn matrices. If det B = 0, then AB is never invertible. Question 4 Let A, B be two 2 x 2 matrices with det A = 3 and det B = -2. What is det(AB-¹)? Question 5 Suppose A and B are 3 x 3 matrices with |A| = 4 and |B| = 2. Compute (1) |AB|, (2) |A2B-¹|, (3) |3A-¹(B-¹)-¹|.
Question 6 Determine if the following subset is a subspace. Justify your an- swer. The set of polynomials p(t) with p(0) = 2 as a subset of P. In other words, H = {p(t) = Pp(0) = 2}. • The set of 2 x 2 matrices with only 0 along the main diagonal as a subset of M2x2. • {(1, 12, 13) Є R³: £1 + 4x2 + 2x3 = 0}. • {(x1, 12, 13) E R³: x1 + 4x2 + 2x3 = 6}. Question 7 Let H be the subset of R4 such that Ha subspace of R4? Justify your answer. x1+x2 x3 + x4 = 0 Is . 21 - x2 x3 x4 = 0 - 3 4 0 7 1 -52 -2 Question 8 Let A = find null space, column space and -1 4 0 3 -1 2 2 row space of A and identify their basis. Question 9 (True or False) If A = b has a solution then be Col(A). Question 10 (True or False) Let A be a 3×4 matrix, then the set of solutions of Ax = b must be a subspace of R4. Question 1 Let A = [2 4 1 7 3 -2 3 0 7-1 -5 4 " write down the cofactor expansion 1 2 -5 of det A with respect to the third column. You do not need to compute. a b C Question 2 Suppose d 9 - - 2a d 2b e 2c-f e f 4. Compute d-5g e-5h f-5i -3g -3h -3i h i Question 3 (True or False) Let A, B be two nxn matrices. If det B = 0, then AB is never invertible. Question 4 Let A, B be two 2 x 2 matrices with det A = 3 and det B = -2. What is det(AB-¹)? Question 5 Suppose A and B are 3 x 3 matrices with |A| = 4 and |B| = 2. Compute (1) |AB|, (2) |A2B-¹|, (3) |3A-¹(B-¹)-¹|.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Transcribed Image Text:Question 6 Determine if the following subset is a subspace. Justify your an-
swer.
The set of polynomials p(t) with p(0) = 2 as a subset of P. In other words,
H = {p(t) = Pp(0) = 2}.
• The set of 2 x 2 matrices with only 0 along the main diagonal as a subset
of M2x2.
• {(1, 12, 13) Є R³: £1 + 4x2 + 2x3 = 0}.
• {(x1, 12, 13) E R³: x1 + 4x2 + 2x3 = 6}.
Question 7 Let H be the subset of R4 such that
Ha subspace of R4? Justify your answer.
x1+x2 x3 + x4 = 0
Is
.
21
-
x2 x3 x4 = 0
-
3
4
0
7
1
-52
-2
Question 8 Let A =
find null space, column space and
-1
4
0
3
-1 2
2
row space of A and identify their basis.
Question 9 (True or False) If A = b has a solution then be Col(A).
Question 10 (True or False) Let A be a 3×4 matrix, then the set of solutions
of Ax = b must be a subspace of R4.
Transcribed Image Text:Question 1 Let A =
[2
4
1
7
3 -2
3 0
7-1
-5 4
"
write down the cofactor expansion
1
2 -5
of det A with respect to the third column. You do not need to compute.
a b C
Question 2 Suppose d
9
-
-
2a d 2b e 2c-f
e f 4. Compute d-5g e-5h f-5i
-3g -3h -3i
h i
Question 3 (True or False) Let A, B be two nxn matrices. If det B = 0, then
AB is never invertible.
Question 4 Let A, B be two 2 x 2 matrices with det A = 3 and det B = -2.
What is det(AB-¹)?
Question 5 Suppose A and B are 3 x 3 matrices with |A| = 4 and |B| = 2.
Compute
(1) |AB|,
(2) |A2B-¹|,
(3) |3A-¹(B-¹)-¹|.
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