GATE | GATE-CS-2015 (Set 1) | Question 65
In the LU decomposition of the matrix
| 2 2 | | 4 9 |
, if the diagonal elements of U are both 1, then the lower diagonal entry l22 of L is
(A) 4
(B) 5
(C) 6
(D) 7
Answer: (B)
Explanation: LU decomposition (where ‘LU’ stands for ‘lower upper’, and also called LU factorization) factors a matrix as the product of a lower triangular matrix and an upper triangular matrix.
| 2 2 | = | l11 0 | * | 1 u12 | | 4 9 | | l21 l22 | | 0 1 | l21 * u12 + l22 * 1 = 9 ------ (1) We need to find l21 and u12 l21 *Â 1 + l22 * 0Â = 4 l21 = 4 l11 * U12 + 0 * 1 = 2 l11 = 2 U12 = 1 Putting value of l21 and u12 in (1), we get 4 * 1 + l22 * 1 = 9 l22 = 5
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