Q2) LU Decomposition, Vector Spaces and LT [1 i Find the LU decomposition of the matrix A = 0 1] a a a when it exists. b b a For which real numbers a and b does it exist? ii Find the dimension of the vector space spanned by the vectors {[1, 1, -2,0, 1], [1, 2, 0, -4, 1], [0, 1, 3, -3, 2], [2, 3, 0, -2,0]} and find a basis for the space. (1) iii Suppose that A is a matrix such that the complete solution to 4 Ax = 1 is of the form : x=1+c2 ,CER 8+8 (a) What can be said about the columns of matrix A? (b) Find the dimension of null space and rank of matrix A.
Q2) LU Decomposition, Vector Spaces and LT [1 i Find the LU decomposition of the matrix A = 0 1] a a a when it exists. b b a For which real numbers a and b does it exist? ii Find the dimension of the vector space spanned by the vectors {[1, 1, -2,0, 1], [1, 2, 0, -4, 1], [0, 1, 3, -3, 2], [2, 3, 0, -2,0]} and find a basis for the space. (1) iii Suppose that A is a matrix such that the complete solution to 4 Ax = 1 is of the form : x=1+c2 ,CER 8+8 (a) What can be said about the columns of matrix A? (b) Find the dimension of null space and rank of matrix A.
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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![Q2) LU Decomposition, Vector Spaces and LT
1 0 1]
i Find the LU decomposition of the matrix A =
a
a a when it exists.
b b a
For which real numbers a and b does it exist?
ii Find the dimension of the vector space spanned by the vectors {[1, 1, -2,0, 1],
[1, 2, 0, 4, 1], [0, 1, 3, -3, 2], [2, 3, 0, -2,0]} and find a basis for the space.
(1)
-
iii Suppose that A is a matrix such that the complete solution to
4
Ax =
1
is of the form :
0
0
x = 1 +c2,cER
8+8
(a) What can be said about the columns of matrix A?
(b) Find the dimension of null space and rank of matrix A.
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d3259e8-1f86-4724-8807-f28d8243a086%2F42e144ba-c0eb-4ef2-9c8e-d82123203de0%2Fu8nnrk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q2) LU Decomposition, Vector Spaces and LT
1 0 1]
i Find the LU decomposition of the matrix A =
a
a a when it exists.
b b a
For which real numbers a and b does it exist?
ii Find the dimension of the vector space spanned by the vectors {[1, 1, -2,0, 1],
[1, 2, 0, 4, 1], [0, 1, 3, -3, 2], [2, 3, 0, -2,0]} and find a basis for the space.
(1)
-
iii Suppose that A is a matrix such that the complete solution to
4
Ax =
1
is of the form :
0
0
x = 1 +c2,cER
8+8
(a) What can be said about the columns of matrix A?
(b) Find the dimension of null space and rank of matrix A.
-
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