Question 1
What defines the kernel of a linear transformation T?
Question 2
Which type of vector do you get by row reducing A augmented with the zero vector?
Question 3
What must be true for a vector u to be in the null space of matrix A?
Question 4
What are the free variables in the null space example given for the matrix A = [ [ 1, 0, 3, 4 ], [ 0, 1, 4, -1 ], [ 0, 2, 0, 6 ] ]?
Question 5
To prove that a given vector is in the null space of a matrix, what operation should be performed?
Question 6
Which theorem asserts that the column space of an m by n matrix A is a subspace of R^m?
Question 7
What does the range of a linear transformation T represent?
Question 8
What is the definition of the column space of a matrix A?
Question 9
Which operation can determine if a vector u is in the column space of A?
Question 10
Given the matrix A = [ [ 2, -6, 12 ], [ -3, 9, 9 ], [ 0, 0, 1 ] ], why does the vector u = [ 3, 1, 0 ] not belong to the column space of A?
Question 11
If A is an m by n matrix, the column space of A is a subspace of which space?
Question 12
How do you express a set W that spans vectors in terms of matrix A?
Question 13
Which of the following vectors is guaranteed to be in the column space of A?
Question 14
If given x4 = 2, what is one example vector in the null space derived from the matrix [ [ 1, 0, 3, 4 ], [ 0, 1, 4, -1 ], [ 0, 2, 0, 6 ] ]?
Question 15
What are the key properties of a linear transformation?