Solving Systems of Equations

The video tutorial explains how to determine if a vector is spanned by a set of vectors by expressing it as a linear combination of the vectors in the set. It involves solving a vector equation using scalar multiplication and forming a system of equations. The tutorial demonstrates solving the system using both direct substitution and the augmented matrix method, verifying the solution, and concluding that the vector is indeed spanned by the set.

What is the main goal of the problem discussed in the video?

• To find the angle between two vectors

• To calculate the dot product of two vectors

• To determine if a vector is spanned by a set of vectors

• To find the magnitude of a vector

What must exist for a vector to be a linear combination of other vectors?

• An orthogonal set of vectors

• A zero vector

• Scalars that satisfy the vector equation

• A unique solution

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CCSS.8.EE.C.8B

How is the first equation in the system of equations solved?

• By adding both sides

• By multiplying both sides by zero

• By dividing both sides by negative two

• By subtracting both sides

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CCSS.8.EE.C.8B

What is the value of c sub two after solving the first equation?

• Fourteen

• Zero

• Negative seven

• Seven

What is the next step after finding c sub two?

• Check the augmented matrix

• Verify the solution with the third equation

• Solve for c sub one using the second equation

• Multiply the vectors

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CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

What is the purpose of verifying the solution with the third equation?

• To find a new solution

• To ensure the solution satisfies all equations

• To eliminate one of the variables

• To simplify the system

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CCSS.8.EE.C.7B

What is the result of the verification process?

• The solution is incorrect

• The solution is partially correct

• The solution needs adjustment

• The solution is verified as correct

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What is the purpose of using an augmented matrix in this context?

• To find the inverse of a matrix

• To calculate the cross product

• To find the determinant

• To solve the system of equations

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CCSS.8.EE.C.8B

What does the row of zeros in the augmented matrix indicate?

• No solution exists

• Infinite solutions exist

• The solution is consistent

• The system is overdetermined

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CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

What are the final values of c sub one and c sub two?

• c sub one = 5, c sub two = -6

• c sub one = 7, c sub two = -6

• c sub one = 6, c sub two = -7

• c sub one = -6, c sub two = 7

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CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B