Indian Institute of Technology Jodhpur
Applied Mathematics and Statistics
Trimester-1 (Sep. 2023)
Assignment-2
10 pts.
Let L, U, D, and P denote a lower triangular, an upper triangular, a diagonal, and a
permutation matrix respectively.
1. Let L be the following matrix with 1’s on

1
L = 3
4
the diagonal:

0 0
1 0 .
5 1
Prove that L−1 has also 1’s on diagonal. (Use Gauss-Jordan elimination)
2. Factor A into LU , where


1 0 1
A = 2 2 2 .
3 4 5
What is the new U in A = LDU ?
3. If A and B are symmetric, then which of the following matrices are certainly symmetric ?
(a) A2 − B 2
(b) (A + B)(A − B)
(c) ABAB
4. Factor the following symmetric matrix A into the form LDU, where
1 b
A=
.
b c
What is special about U in this case ?
5. Factor P A = LU , where


0 1 1
A = 1 2 1 .
2 7 9
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