Consider solving the following system of simultaneous equations using LU decomposition x 1 + x 2 - 2x 3 = 4 x1 + 3x2 - x3 = 7 2x1 + x2 - 5x3 = 7 where L and U are denoted as L = \left(\begin{array}{c}L_{11\end{array} , 0 , 0 ; \text{ L_{21}} , L_{22} , 0 ; \text{ L_{31}} , L_{32} , L_{33} ; )}, U = \left(\begin{array}{c}U_{11\end{array} , U_{12} , U_{13} ; \text{ 0} , U_{22} , U_{23} ; \text{ 0} , 0 , U_{33} ; )} Which one of the following is the correct combination of values for L 32 , U 33 , and x 1 ?

Correct Answer is : L32 = −12, U33 = −12, x1 = 0

L 32 = 2, U 33 = −\frac{1}{2}, x 1 = -1

L32 = −\frac{1}{2}, U33 = 2, x1 = 0

L32 = −\frac{1}{2}, U33 = −\frac{1}{2}, x1 = 0

GATE Computer Science (CS) 2022 Shift 1 Solved Paper

Question : 44 of 65

Marks: +1, -0

Consider solving the following system of simultaneous equations using LU decomposition
x₁ + x₂ - 2x₃ = 4
x1 + 3x2 - x3 = 7
2x1 + x2 - 5x3 = 7
where L and U are denoted as

L = {(\table L_{11} , 0 , 0 ; \text" L_{21}" , L_{22} , 0 ; \text" L_{31}" , L_{32} , L_{33} ; )}

U = {(\table U_{11} , U_{12} , U_{13} ; \text" 0" , U_{22} , U_{23} ; \text" 0" , 0 , U_{33} ; )}

Which one of the following is the correct combination of values for L₃₂, U₃₃, and x₁ ?

L₃₂ = 2, U₃₃ = $−\;{1}/{2}$ , x₁ = -1
L32 = 2, U33 = 2, x1 = -1
L32 = $−\;{1}/{2}$ , U33 = 2, x1 = 0
L32 = $−\;{1}/{2}$ , U33 = $−\;{1}/{2}$ , x1 = 0

Validate

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