Show that a tridiagonal matrix can be written in the form A matrix that has zeros in

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Show that a tridiagonal matrix can be written in the form

[a b C a C3 0 0 b a3 b3 Cn-1 1-1 Cn ba b-1 an

|| X 4 121 122 132 0 112 1 0 0 133 In.n-1 Inn U23 1 34 0 1 u, 'n-1,n 1

A matrix that has zeros in every position below the diagonal is called an upper-triangular matrix and one with zeros everywhere above the diagonal is called a lower-triangular matrix. A matrix that only has non-zero elements in certain diagonal lines is called a banded matrix. In this case we have shown that a tridiagonal matrix can be written as the product of a lower-triangular banded matrix and an upper-triangular banded matrix.

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