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In this lesson, we will learn how to find the general solution of a system of linear equations and determine a basis for its solution space.

Q1:

Find a basis for the solution space of the system

Q2:

Find the general solution of the following system of linear equations: and then find a basis for its solution space.

Q3:

Find the general solution of the system of linear equations and hence find a basis for its solution space.

Q4:

Q5:

Let 𝑉 be the space of polynomials in the variable 𝑥 that have degree less than 4. Is 𝑥 + 1 , 𝑥 + 𝑥 + 2 𝑥 , 𝑥 + 𝑥 , 𝑥 + 𝑥 + 𝑥 3 2 2 3 2 a basis for this space?

Q6:

Find the general solution to the system of linear equations and hence find a basis for its solution space.

Q7:

Q8:

Find the general solution of the system of linear equations and then find a basis for its solution space.

Q9:

Q10:

Suppose that 𝐴 and 𝐵 are 𝑚 × 𝑚 matrices and v is a vector in the nullspace of 𝐴 . Consider this statement: Which of the following is true?

Q11:

Suppose that the columns of an 𝑚 × 𝑚 matrix 𝐴 are linearly independent. Then, which of the following statements is always true?

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