Exercise · ZW-CHOLESKY-FACTORIZATION-007 · ★★☆ Intermediate
If \(a_{22}=10\) and \(l_{21}=3\), what is \(l_{22}\)?
Choose one option.
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- D. 1
Explanation
Since \(l_{22}=\sqrt{a_{22}-l_{21}^{2}}=\sqrt{10-9}=1\). The root of 10 forgets to subtract \(l_{21}^{2}\), the root of 19 adds instead of subtracting, and 7 subtracts \(l_{21}\) without squaring or taking a root.
Review the concept: Cholesky factorization
The Cholesky factorization decomposes a symmetric positive definite matrix \(A\) as \(A = LL^{T}\), where \(L\) is lower triangular with positive diagonal.
\[A = LL^{T}, \; l_{jj} = \sqrt{a_{jj} - \sum_{k
More practice problems: cholesky factorization
- ZW-CHOLESKY-FACTORIZATION-001 What property must a matrix A have to apply the Cholesky factorization?
- ZW-CHOLESKY-FACTORIZATION-002 What form does the factor L have in A = LL^T?
- ZW-CHOLESKY-FACTORIZATION-003 If L is the Cholesky factor, what does the equality A = LL^T express?
- ZW-CHOLESKY-FACTORIZATION-004 What is the element l_11 of the Cholesky factor when a_11=9?
- ZW-CHOLESKY-FACTORIZATION-005 What is the relation between Cholesky and LU for a symmetric positive definite matrix?
- ZW-CHOLESKY-FACTORIZATION-006 Compute l_11 and l_21 for A=[4 2; 2 5].
- ZW-CHOLESKY-FACTORIZATION-008 For A=[9 3; 3 5], what is the factor L?
- ZW-CHOLESKY-FACTORIZATION-009 If L=[2 0; 1 2], what is the product LL^T?
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