Module 5 Linear Algebra: Definitions and Theorems

The set of all linear combination of rows of A

• Row(A)

• Coll(A)

• Null(A)

The set of all linear combination of columns of A

• Row(A)

• Coll(A)

• Null(A)

The solution set of the homogeneous SLE Ax = 0

• Row(A)

• Coll(A)

• Null(A)

The dimension of the row space or column space of matrix A is called the ... of A.

• Rank

• Nullity

The dimension of the null space of matrix A is called the ... of A

• Rank

• Nullity

Elementary row operations do not change the null space of a matrix

• True

• False

Elementary row operations do not change the row space of a matrix.

• True

• False

If A and B are row equivalent matrices, then a set that consists of (all or several) column vectors of A are linearly independent if and only if corresponding column vectors of B are linearly independent.

• True

• False

If A and B are row equivalent matrices, then a set that consists of (all or several) column vectors of A is a basis of column space of A if and only if corresponding column vectors of B forms a basis of column space of B.

• True

• False

If R is a matrix in row-echelon form, then row vectors that contain a leading 1 (non zero row vectors) forms a basis for the row space of R, and column vectors that contain a leading 1 forms a basis for the column space of R.

• True

• False