# What if a matrix has more rows than columns?

## What if a matrix has more rows than columns?

A matrix is full row rank when each of the rows of the matrix are linearly independent and full column rank when each of the columns of the matrix are linearly independent. So if there are more rows than columns (m>n), then the matrix is full rank if the matrix is full column rank.

**What is an NXM matrix?**

A matrix of order (m x n) becomes of order (n x m) when transposed. For example, if a (2 x 3) matrix is defined by. Then the transpose of A, denoted by A’, is now (3 x 2)

### Can a matrix have more pivot columns than rows?

The rank of a matrix is the number of pivots in its reduced row-echelon form. Note that the rank of an m × n matrix cannot be bigger than m, since you can’t have more than one pivot per row.

**How many rows and columns are in an m x n matrix?**

I like to remember this as being in REVERSE alphabetical order – Rows by Columns, or R first then C. However, in Boyce & DiPrima’s book “Elementary Differential Equations and Boundary Value Problems” an m x n matrix has m vertical columns and n horizontal rows. However, when addressing elements within a matrix, it’s the opposite.

#### How to determine row space and column space of a matrix?

Row Space and Column Space of a Matrix. Since the column space of A consists precisely of those vectors b such that A x = b is a solvable system, one way to determine a basis for CS(A) would be to first find the space of all vectors b such that A x = b is consistent, then constructing a basis for this space.

**When to multiply one matrix by another matrix?**

In the following example, the scalar value is 3 . When can you multiply one matrix by another matrix? You can multiply two matrices if, and only if, the number of columns in the first matrix equals the number of rows in the second matrix. (Link on columns vs rows )

## Is the statement ” two matrices are row equivalent ” true or false?

False, because if two matrices are row equivalent it means that there exists a sequence of row operations that transforms one matrix to the other Is the statement “Elementary row operations on an augmented matrix never change the solution set of the associated linear system” true or false? Explain.