# I was given a math question on matrices where i was asked to multiply a 2x2 matrix by a 3x3 matrix but couldn't come up with an answer. It's confusing, a little help here please. Or should i just say its undefine??

Mar 16, 2017

undefine

#### Explanation:

The product of matrices only can be define when the number of columns in the first matric is equals to the number of rows in the second matric.

for example

$M {1}_{2 X 3} \cdot M {2}_{3 X 2} = {M}_{2 X 2}$

Matric M1 has 3 columns and M2 has 3 rows. Then it can be defined

therefore for
${M}_{2 X 2} \cdot {M}_{3 X 3}$ = unable to define because they have different number of column for the first matric and row second matric.

Mar 16, 2017

You just cannot multiply a $2 \times 2$ matrix with a $3 \times 3$ matrix and can say that multipication of such matrices is not defined as number of columns of the first is not equal to number of rows of the second matrix.

#### Explanation:

You just cannot multiply a $2 \times 2$ matrix with a $3 \times 3$ matrix.

You can only two matrices if number of columns of the first matrix is equal to number of rows of the second matrix.

i.e. you can only multiply a $l \times m$ matrix with a $m \times n$ matrix and the result will be a $l \times n$ matrix.

This is an important part of the process of multiplication.

Let us have a $2 \times 3$ matrix $\left(\begin{matrix}{a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23}\end{matrix}\right)$ and a $3 \times 4$ matrix $\left(\begin{matrix}{b}_{11} & {b}_{12} & {b}_{13} & {b}_{14} \\ {b}_{21} & {b}_{22} & {b}_{23} & {b}_{24} \\ {b}_{31} & {b}_{32} & {b}_{33} & {b}_{34}\end{matrix}\right)$t

The result is a $2 \times 4$ matrix $\left(\begin{matrix}{x}_{11} & {x}_{12} & {x}_{13} & {x}_{14} \\ {x}_{21} & {x}_{22} & {x}_{23} & {x}_{24}\end{matrix}\right)$,

where ${x}_{11}$ is obtained by multiplying the three elements of first row with the three elements of first column of second matrix.

If number of columns of the first matrix are not equal to number of rows of the second matrix, which is so in the case mentioned by you, this is not possible and hence, you cannot multiply a $2 \times 2$ matrix with a $3 \times 3$ matrix,

and you can say multiplication of such matrices is not defined.