## Answer in 60

### Input

### Result

### Row-reduced matrix

**Key moments in video**

From 00:32 — Procedure for finding a basis for a null space

From 01:05 — Reduced Row Echelon Form

From 03:03 — How to get the basis

**Key moments in video**

From 04:51 — Definition of the Null Space

From 06:41 — Finding a basis for the Infinite Collection of Vectors

From 08:25 — Determining the Dimension of the Null Space

From 09:08 — Finding the Dimension of the Space

**Key moments in video**

From 00:15 — Finding the row reduced echelon form

From 02:35 — How to Recognize the Independent and Dependent Variables

From 03:33 — Substitute a 1 for Independent Variables

From 04:40 — Find the nullity of the matrix

## Related querie

### What is the basis for the column space?

A basis for the column space of a matrix A is **the columns of A corresponding to columns of rref(A) that contain leading ones**. The solution to Ax = 0 (which can be easily obtained from rref(A) by augmenting it with a column of zeros) will be an arbitrary linear combination of vectors.

### What is the basis of the zero vector space?

Trivial or zero vector space

A basis for this vector space is **the empty set**, so that {0} is the 0-dimensional vector space over F. Every vector space over F contains a subspace isomorphic to this one. The zero vector space is conceptually different from the null space of a linear operator L, which is the kernel of L.

### What is the basis for the null space?

In general, if A is in RREF, then a basis for the nullspace of A can be built up by doing the following: **For each free variable, set it to 1 and the rest of the free variables to zero and solve for the pivot variables**. The resulting solution will give a vector to be included in the basis.

### What is the null space of a vector?

The null space of A is **all the vectors x for which Ax = 0**, and it is denoted by null(A). This means that to check to see if a vector x is in the null space we need only to compute Ax and see if it is the zero vector.

### What is null space in linear algebra?

In mathematics, the kernel of a linear map, also known as the null space or nullspace, is **the linear subspace of the domain of the map which is mapped to the zero vector**.

### What is a basis in a vector space?

In mathematics, **a set B of vectors in a vector space V is called a basis if every element of V may be written in a unique way as a finite linear combination of elements of B**. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B.

### Does zero vector have a basis?

Vector space for {0} – why is empty set {} a basis, but {0} is not? A basis is a collection of vectors that is linearly independent and spans the entire space. Thus **the empty set is basis**, since it is trivially linearly independent and spans the entire space (the empty sum over no vectors is zero).

### What is the zero vector of a vector space?

Vector Spaces

The zero vector in a vector space is unique. The additive inverse of any vector v in a vector space is unique and is equal to **âˆ’ 1 Â· v**. A nonempty subset of a vector space is a subspace of if and only if is closed under addition and scalar multiplication.

### What is a basis for the column space?

A basis for the column space of a matrix A is **the columns of A corresponding to columns of rref(A) that contain leading ones**. The solution to Ax = 0 (which can be easily obtained from rref(A) by augmenting it with a column of zeros) will be an arbitrary linear combination of vectors.

### What is meant by null space?

Definition of null-space

: **a subspace of a vector space consisting of vectors that under a given linear transformation are mapped onto zero**.