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39 lines
1.1 KiB
Markdown
39 lines
1.1 KiB
Markdown
---
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day: [[2022-05-02]]
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tags: #linear_algebra
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cards-deck: default_obsidian
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---
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#math/linear_algebra
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## system of linear equations
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### definition
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#card
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a collection of equations that we try to solve simultaneously
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![[Pasted image 20220502144937.png]]
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^1651526044890
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### equivalent if
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#card
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Two systems are equivalent if they have the same solution set. All solutions have to be the same.
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^1651526044960
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### theorem
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#card
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A system can either have:
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- one solution
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- no solution
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- $\infty$ solutions
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![[Pasted image 20220502145609.png]]
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^1651526044967
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[[matrix representation of systems of linear equations]]
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### is it consistent?
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#card/reverse
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a system with one or more solutions is consistent. If it has no solution it's inconsistent.
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[[homogeneous]] systems are all consistent, since the zero solution (trivial solution) is always an answer.
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in the [[matrix representation of systems of linear equations#reduced row echelon form|reduced row echelon form]], a no solution matrix will have zeroes in the bottom row, except the last column. Basically saying, "0=1".
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^1652735881584
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