Linear Algebra Examples

Find the Variables [[3,-4,0],[2,8,-1]]+B=[[0,0,0],[0,0,0]]
Step 1
Find the function rule.
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Step 1.1
Check if the function rule is linear.
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Step 1.1.1
To find if the table follows a function rule, check to see if the values follow the linear form .
Step 1.1.2
Build a set of equations from the table such that .
Step 1.1.3
Calculate the values of and .
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Step 1.1.3.1
Rewrite the equation as .
Step 1.1.3.2
Replace all occurrences of with in each equation.
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Step 1.1.3.2.1
Replace all occurrences of in with .
Step 1.1.3.2.2
Simplify .
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Step 1.1.3.2.2.1
Simplify the left side.
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Step 1.1.3.2.2.1.1
Remove parentheses.
Step 1.1.3.2.2.2
Simplify the right side.
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Step 1.1.3.2.2.2.1
Simplify .
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Step 1.1.3.2.2.2.1.1
Add and .
Step 1.1.3.2.2.2.1.2
Move to the left of .
Step 1.1.3.2.3
Replace all occurrences of in with .
Step 1.1.3.2.4
Simplify .
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Step 1.1.3.2.4.1
Simplify the left side.
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Step 1.1.3.2.4.1.1
Remove parentheses.
Step 1.1.3.2.4.2
Simplify the right side.
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Step 1.1.3.2.4.2.1
Simplify .
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Step 1.1.3.2.4.2.1.1
Add and .
Step 1.1.3.2.4.2.1.2
Move to the left of .
Step 1.1.3.2.5
Replace all occurrences of in with .
Step 1.1.3.2.6
Simplify .
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Step 1.1.3.2.6.1
Simplify the left side.
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Step 1.1.3.2.6.1.1
Remove parentheses.
Step 1.1.3.2.6.2
Simplify the right side.
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Step 1.1.3.2.6.2.1
Simplify .
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Step 1.1.3.2.6.2.1.1
Add and .
Step 1.1.3.2.6.2.1.2
Move to the left of .
Step 1.1.3.2.7
Replace all occurrences of in with .
Step 1.1.3.2.8
Simplify .
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Step 1.1.3.2.8.1
Simplify the left side.
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Step 1.1.3.2.8.1.1
Remove parentheses.
Step 1.1.3.2.8.2
Simplify the right side.
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Step 1.1.3.2.8.2.1
Simplify .
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Step 1.1.3.2.8.2.1.1
Add and .
Step 1.1.3.2.8.2.1.2
Move to the left of .
Step 1.1.3.2.9
Replace all occurrences of in with .
Step 1.1.3.2.10
Simplify .
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Step 1.1.3.2.10.1
Simplify the left side.
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Step 1.1.3.2.10.1.1
Remove parentheses.
Step 1.1.3.2.10.2
Simplify the right side.
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Step 1.1.3.2.10.2.1
Simplify .
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Step 1.1.3.2.10.2.1.1
Add and .
Step 1.1.3.2.10.2.1.2
Move to the left of .
Step 1.1.3.2.10.2.1.3
Rewrite as .
Step 1.1.3.3
Solve for in .
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Step 1.1.3.3.1
Rewrite the equation as .
Step 1.1.3.3.2
Divide each term in by and simplify.
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Step 1.1.3.3.2.1
Divide each term in by .
Step 1.1.3.3.2.2
Simplify the left side.
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Step 1.1.3.3.2.2.1
Dividing two negative values results in a positive value.
Step 1.1.3.3.2.2.2
Divide by .
Step 1.1.3.3.2.3
Simplify the right side.
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Step 1.1.3.3.2.3.1
Divide by .
Step 1.1.3.4
Replace all occurrences of with in each equation.
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Step 1.1.3.4.1
Replace all occurrences of in with .
Step 1.1.3.4.2
Simplify the right side.
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Step 1.1.3.4.2.1
Multiply by .
Step 1.1.3.4.3
Replace all occurrences of in with .
Step 1.1.3.4.4
Simplify the right side.
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Step 1.1.3.4.4.1
Multiply by .
Step 1.1.3.4.5
Replace all occurrences of in with .
Step 1.1.3.4.6
Simplify the right side.
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Step 1.1.3.4.6.1
Multiply by .
Step 1.1.3.4.7
Replace all occurrences of in with .
Step 1.1.3.4.8
Simplify the right side.
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Step 1.1.3.4.8.1
Multiply by .
Step 1.1.3.5
Remove any equations from the system that are always true.
Step 1.1.3.6
List all of the solutions.
Step 1.1.4
Calculate the value of using each value in the relation and compare this value to the given value in the relation.
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Step 1.1.4.1
Calculate the value of when , , and .
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Step 1.1.4.1.1
Multiply by .
Step 1.1.4.1.2
Add and .
Step 1.1.4.2
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Step 1.1.4.3
Calculate the value of when , , and .
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Step 1.1.4.3.1
Multiply by .
Step 1.1.4.3.2
Add and .
Step 1.1.4.4
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Step 1.1.4.5
Calculate the value of when , , and .
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Step 1.1.4.5.1
Multiply by .
Step 1.1.4.5.2
Add and .
Step 1.1.4.6
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Step 1.1.4.7
Calculate the value of when , , and .
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Step 1.1.4.7.1
Multiply by .
Step 1.1.4.7.2
Add and .
Step 1.1.4.8
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Step 1.1.4.9
Calculate the value of when , , and .
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Step 1.1.4.9.1
Multiply by .
Step 1.1.4.9.2
Add and .
Step 1.1.4.10
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Step 1.1.4.11
Calculate the value of when , , and .
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Step 1.1.4.11.1
Multiply by .
Step 1.1.4.11.2
Add and .
Step 1.1.4.12
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Step 1.1.4.13
Since for the corresponding values, the function is linear.
The function is linear
The function is linear
The function is linear
Step 1.2
Since all , the function is linear and follows the form .
Step 2
List all of the solutions.
Step 3
Nothing further can be done with this topic. Please check the expression entered or try another topic.