Prove that the matrix A = [0 1 1 0] has no LU factorization, i. e., no

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Prove that the matrix A = [0 1 1 0] has no LU factorization, i. e., no lower triangular matrix L and upper triangular matrix U exist, such that A = LU. Hint: Assume that there is an LU decomposition [l11 0 l21 l22] [u11 u12 0 u22] = [0 1 1 0] and arrive at a contradiction!

Prove that the matrix A = [0 1 1 0] has no LU factorization, i. e., no lower triangular matrix L and upper triangular matrix U exist, such that A = LU. Hint: Assume that there is an LU decomposition [l11 0 l21 l22] [u11 u12 0 u22] = [0 1 1 0] and arrive at a contradiction!

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Prove that the matrix

A = [\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}]

has no

L U

factorization, i.e., no lower triangular matrix

L

and upper triangular matrix

U

exist, such that

A = L U

. Hint: Assume that there is an

L U

decomposition

[\begin{array}{cc} l_{11} & 0 \\ l_{21} & l_{22} \end{array}] [\begin{array}{cc} u_{11} & u_{12} \\ 0 & u_{22} \end{array}] = [\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}]

and arrive at a contradiction!

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