1. Let the matrix42be factorized in LDU form such that U =12Then, M120 16.C.d. 22 0 02. The matrix41 0has the inverse matrit20 1200/2 0 0/2 0 0-1/2 0 01/4 I 0-1/2 0 14.-/4 10/2 0 1C.2 1 0-2 01-I 0 11.3. The system11-8x=b has exactly one solution for any be R' whena0 a-Ba *Bd aß 0KAHRABTE-3 -2 14. Let B= 08 8I C(B) =N(A) then matrix A has this minimum number of rows:0 2 -23 3 06. 23. Knowing that the coefficient matrix of the system d= can be written in the form 4-LU, andthat Gauss elimination transforms the system into Ug =c, then6. Given A is a 4x3 matrix, the matrixis singular for any 4x1 vector s that satisfiesA ceC(A)ceC(4)7. Givep that D-then N(D) containsAll vectors thatbelang to bothN(A) and N(8)& All vectors thatbelong to N(A)N(B). All vectors thatbelong toN(A+ B)4 All vectors thatbelong toN(AB)

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Answered: 200 2. The matrix4 1 0has the inverse…

200 2. The matrix4 1 0has the inverse matrit 20 1 2007 /2 0 07 -/4 10 /2 0 1 /2 0 0 -1/2 0 0 410 6. 2 10 d. 1/4 I0 C. -2 01 -1 0 1 -1/2 0 1 3.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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Question

1. Let the matrix
42
be factorized in LDU form such that U =
12
Then, M12
0 1
6.
C.
d. 2
2 0 0
2. The matrix41 0has the inverse matrit
20 1
200
/2 0 0
/2 0 0
-1/2 0 0
1/4 I 0
-1/2 0 1
4.
-/4 10
/2 0 1
C.
2 1 0
-2 01
-I 0 1
1.
3. The system1
1-8x=b has exactly one solution for any be R' when
a
0 a-B
a *B
d aß 0
KAHRABTE
-3 -2 1
4. Let B= 0
8 8I C(B) =N(A) then matrix A has this minimum number of rows:
0 2 -2
3 3 0
6. 2
3. Knowing that the coefficient matrix of the system d= can be written in the form 4-LU, and
that Gauss elimination transforms the system into Ug =c, then
6. Given A is a 4x3 matrix, the matrix
is singular for any 4x1 vector s that satisfies
A ceC(A)
ceC(4)
7. Givep that D-
then N(D) contains
All vectors that
belang to both
N(A) and N(8)
& All vectors that
belong to N(A)
N(B)
. All vectors that
belong to
N(A+ B)
4 All vectors that
belong to
N(AB)

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