Algebra lineare Esempi

Trovare il Nucleo [[63,-36,45,-27,54],[-81,54,-63,45,-72],[-36,63,-54,72,-45],[45,-18,45,-9,36],[27,-54,-54,-63,36],[-27,-45,18,-36,81],[-63,45,72,72,27]]
Passaggio 1
Write as an augmented matrix for .
Passaggio 2
Trova la forma ridotta a scala per righe di Echelon.
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Passaggio 2.1
Multiply each element of by to make the entry at a .
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Passaggio 2.1.1
Multiply each element of by to make the entry at a .
Passaggio 2.1.2
Semplifica .
Passaggio 2.2
Perform the row operation to make the entry at a .
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Passaggio 2.2.1
Perform the row operation to make the entry at a .
Passaggio 2.2.2
Semplifica .
Passaggio 2.3
Perform the row operation to make the entry at a .
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Passaggio 2.3.1
Perform the row operation to make the entry at a .
Passaggio 2.3.2
Semplifica .
Passaggio 2.4
Perform the row operation to make the entry at a .
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Passaggio 2.4.1
Perform the row operation to make the entry at a .
Passaggio 2.4.2
Semplifica .
Passaggio 2.5
Perform the row operation to make the entry at a .
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Passaggio 2.5.1
Perform the row operation to make the entry at a .
Passaggio 2.5.2
Semplifica .
Passaggio 2.6
Perform the row operation to make the entry at a .
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Passaggio 2.6.1
Perform the row operation to make the entry at a .
Passaggio 2.6.2
Semplifica .
Passaggio 2.7
Perform the row operation to make the entry at a .
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Passaggio 2.7.1
Perform the row operation to make the entry at a .
Passaggio 2.7.2
Semplifica .
Passaggio 2.8
Multiply each element of by to make the entry at a .
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Passaggio 2.8.1
Multiply each element of by to make the entry at a .
Passaggio 2.8.2
Semplifica .
Passaggio 2.9
Perform the row operation to make the entry at a .
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Passaggio 2.9.1
Perform the row operation to make the entry at a .
Passaggio 2.9.2
Semplifica .
Passaggio 2.10
Perform the row operation to make the entry at a .
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Passaggio 2.10.1
Perform the row operation to make the entry at a .
Passaggio 2.10.2
Semplifica .
Passaggio 2.11
Perform the row operation to make the entry at a .
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Passaggio 2.11.1
Perform the row operation to make the entry at a .
Passaggio 2.11.2
Semplifica .
Passaggio 2.12
Perform the row operation to make the entry at a .
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Passaggio 2.12.1
Perform the row operation to make the entry at a .
Passaggio 2.12.2
Semplifica .
Passaggio 2.13
Perform the row operation to make the entry at a .
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Passaggio 2.13.1
Perform the row operation to make the entry at a .
Passaggio 2.13.2
Semplifica .
Passaggio 2.14
Swap with to put a nonzero entry at .
Passaggio 2.15
Multiply each element of by to make the entry at a .
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Passaggio 2.15.1
Multiply each element of by to make the entry at a .
Passaggio 2.15.2
Semplifica .
Passaggio 2.16
Perform the row operation to make the entry at a .
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Passaggio 2.16.1
Perform the row operation to make the entry at a .
Passaggio 2.16.2
Semplifica .
Passaggio 2.17
Perform the row operation to make the entry at a .
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Passaggio 2.17.1
Perform the row operation to make the entry at a .
Passaggio 2.17.2
Semplifica .
Passaggio 2.18
Perform the row operation to make the entry at a .
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Passaggio 2.18.1
Perform the row operation to make the entry at a .
Passaggio 2.18.2
Semplifica .
Passaggio 2.19
Swap with to put a nonzero entry at .
Passaggio 2.20
Multiply each element of by to make the entry at a .
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Passaggio 2.20.1
Multiply each element of by to make the entry at a .
Passaggio 2.20.2
Semplifica .
Passaggio 2.21
Perform the row operation to make the entry at a .
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Passaggio 2.21.1
Perform the row operation to make the entry at a .
Passaggio 2.21.2
Semplifica .
Passaggio 2.22
Perform the row operation to make the entry at a .
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Passaggio 2.22.1
Perform the row operation to make the entry at a .
Passaggio 2.22.2
Semplifica .
Passaggio 2.23
Perform the row operation to make the entry at a .
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Passaggio 2.23.1
Perform the row operation to make the entry at a .
Passaggio 2.23.2
Semplifica .
Passaggio 2.24
Perform the row operation to make the entry at a .
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Passaggio 2.24.1
Perform the row operation to make the entry at a .
Passaggio 2.24.2
Semplifica .
Passaggio 2.25
Perform the row operation to make the entry at a .
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Passaggio 2.25.1
Perform the row operation to make the entry at a .
Passaggio 2.25.2
Semplifica .
Passaggio 2.26
Perform the row operation to make the entry at a .
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Passaggio 2.26.1
Perform the row operation to make the entry at a .
Passaggio 2.26.2
Semplifica .
Passaggio 3
Use the result matrix to declare the final solution to the system of equations.
Passaggio 4
Write a solution vector by solving in terms of the free variables in each row.
Passaggio 5
Write the solution as a linear combination of vectors.
Passaggio 6
Write as a solution set.