Answer:
Both the answers are as in the solution.
Step-by-step explanation:
As the given matrix is not in the readable form, a similar question is found online and the solution of which is attached herewith.
Part a:
Given matrix is : A =
Here,
Then, A is non-singular matrix.
Here, A₁₁= 0.
If we write A as LU with L lower triangular matrix and U upper triangular matrix, then A₁₁=L₁₁U₁₁.
So, As
A₁₁ = 0 gives L₁₁U₁₁= 0 ,
This indicates that either L₁₁= 0 or U₁₁ = 0.
If L₁₁= 0 or U₁₁ = 0, this would made the corresponding matrix singular, which contradicts the condition as A is non-singular.
Therefore, A has no LU decomposition.
Part b:
By the implementation of the various row operations
<em>interchange R1 and R2</em>
<em>R3+3R1=R3</em>
<em>R3+(1/3)R2 = R3</em>
Therefore, U = .
Here, LP = E₁₂=E₃₁=-3 &E₃₂=-1/3
So now U is given as