# Worksheet: Basis for the Kernel of a Matrix

Q1:

Find a basis for the solution space of the following system.

• A
• B
• C
• D
• E

Q2:

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

• AThe general solution is . A basis for the solution space is .
• BThe general solution is . A basis for the solution space is .
• CThe general solution is . A basis for the solution space is .
• DThe general solution is . A basis for the solution space is .
• EThe general solution is . A basis for the solution space is .

Q3:

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

• AThe general solution is , and a basis for the solution space is .
• B The general solution is , and a basis for the solution space is .
• CThe general solution is , and a basis for the solution space is .
• DThe general solution is , and a basis for the solution space is .
• E The general solution is , and a basis for the solution space is .

Q4:

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

• AThe general solution is , and a basis for the solution space is .
• B The general solution is , and a basis for the solution space is .
• CThe general solution is , and a basis for the solution space is .
• DThe general solution is , and a basis for the solution space is .
• EThe general solution is , and a basis for the solution space is .

Q5:

Let be the space of polynomials in the variable that have degree less than 4. Is a basis for this space?

• Ayes
• Bno

Q6:

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

• AThe general solution is . A basis for the solution space is .
• BThe general solution is . A basis for the solution space is .
• CThe general solution is . A basis for the solution space is .
• DThe general solution is . A basis for the solution space is .
• EThe general solution is . A basis for the solution space is .

Q7:

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

• AThe general solution is . A basis for the solution space is .
• BThe general solution is . A basis for the solution space is .
• CThe general solution is . A basis for the solution space is .
• DThe general solution is . A basis for the solution space is .
• EThe general solution is . A basis for the solution space is .

Q8:

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

• AThe general solution is . A basis for the solution space is .
• BThe general solution is . A basis for the solution space is .
• CThe general solution is . A basis for the solution space is .
• DThe general solution is . A basis for the solution space is .
• EThe general solution is . A basis for the solution space is .

Q9:

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

• AThe general solution is . A basis for the solution space is .
• BThe general solution is . A basis for the solution space is .
• CThe general solution is . A basis for the solution space is .
• DThe general solution is . A basis for the solution space is .
• EThe general solution is . A basis for the solution space is .