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 *  1 + l22 * 0  = 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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