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m Rollback edit(s) by 2409:4051:2E9D:67F5:0:0:B149:920B (talk): Vandalism (RW 16.1) |
StephanSp3 (talk | contribs) →Forward and back substitution: Remove "Note: errors in formulas below" because no error found |
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\end{matrix}</math>
Observe that the first equation (<math>\ell_{1,1} x_1 = b_1</math>) only involves <math>x_1</math>, and thus one can solve for <math>x_1</math> directly. The second equation only involves <math>x_1</math> and <math>x_2</math>, and thus can be solved once one substitutes in the already solved value for <math>x_1</math>. Continuing in this way, the <math>k</math>-th equation only involves <math>x_1,\dots,x_k</math>, and one can solve for <math>x_k</math> using the previously solved values for <math>x_1,\dots,x_{k-1}</math>. The resulting formulas are:
:<math>\begin{align}
x_1 &= \frac{b_1}{\ell_{1,1}}, \\
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