Find the LU Decomposition of the matrix ( A = begin{bmatrix} 4 & 3 newline 6 & 3 end{bmatrix} )

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Step:1 ：Step 1: Initialize the identity matrix ( I = begin{bmatrix} 1 & 0 newline 0 & 1 end{bmatrix} ) and the matrix ( L = I )Step:2 ：Step 2: Perform row operations to convert ( A ) into an upper triangular matrix ( U ). Multiply row 2 by ( frac{4}{6} ) and subtract row 1 from it. Now, ( U = begin{bmatrix} 4 & 3 newline 0 & -1 end{bmatrix} )Step:3 ：Step 3: Inverse the operations performed on ( A ) to get ( L ). Divide row 2 by ( frac{4}{6} ) and add row 1 to it. Now, ( L = begin{bmatrix} 1 & 0 newline frac{3}{2} & 1 end{bmatrix} )

Answer

Step: 1 ：Step 1: Initialize the identity matrix ( I = begin{bmatrix} 1 & 0 newline 0 & 1 end{bmatrix} ) and the matrix ( L = I )Step: 2 ：Step 2: Perform row operations to convert ( A ) into an upper triangular matrix ( U ). Multiply row 2 by ( frac{4}{6} ) and subtract row 1 from it. Now, ( U = begin{bmatrix} 4 & 3 newline 0 & -1 end{bmatrix} )Step: 3 ：Step 3: Inverse the operations performed on ( A ) to get ( L ). Divide row 2 by ( frac{4}{6} ) and add row 1 to it. Now, ( L = begin{bmatrix} 1 & 0 newline frac{3}{2} & 1 end{bmatrix} )

Find the LU Decomposition of the matrix $A = [\begin{matrix} 4 & 3 \\ 6 & 3 \end{matrix}]$

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Find the LU Decomposition of the matrix $A = [\begin{matrix} 4 & 3 \\ 6 & 3 \end{matrix}]$