What is the Cholesky decomposition of a matrix?

Cholesky decomposition is a method to decompose a symmetric, positive-definite matrix into the product of a lower triangular matrix and its transpose. For the given matrix [9, 15; 15, 50], we find l 22 by ensuring that L × L T = A where A is the original matrix.

How do you calculate |l 22 | in Cholesky decomposition?

To find l 22 , we use the formula: l 22 2 = a 22 - (l 12 ) 2 . For matrix [9, 15; 15, 50], l 12 is the element in the first row and second column. After calculating, we find |l 22 | = 7.

What does 'C) 7' mean in this context?

The correct answer is C) 7. This means that the absolute value of l 22 , which is one of the elements in the lower triangular matrix resulting from Cholesky decomposition, is 7.

Cholesky Decomposition | Matrix Determinant Q27 | GATE Civil 2026 Set-1

Civil Engineering > GATE 2026 SET-1 > Linear Algebra

A matrix is given as:

[9 15]
[15 50]

By performing Cholesky decomposition, |l₂₂| of the lower triangular matrix is ______ (in integer).

Correct : 5

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