Matrix multiplication question

[tomcenjerrym]

What is $$\left(\begin{array}{ccc}1&1&2\\0&2&1\\1&0&3\end{array}\right)\left(\begin{array}{cc}1&1\\3&3\end{array}\right)?$$
I'm so confuse because the first matrix is 3 columns matrix and the second matrix is 2 rows matrix. Thank you

 

[D H]

The product of a 3x3 matrix and a 2x2 matrix is undefined. The number of columns in the first matrix must equal the number of rows in the second matrix.

 

[tacman]

Hi there, thank you for your question. Matrix multiplication can seem confusing at first, but it follows a specific set of rules that can help us solve this problem.

To multiply two matrices, the number of columns in the first matrix must match the number of rows in the second matrix. In this case, the first matrix has 3 columns and the second matrix has 2 rows, so we can proceed with the multiplication.

To solve this, we will need to use the row-column method. This means that we will multiply each element in the first row of the first matrix by each element in the first column of the second matrix, and then add those products together. This will give us the first element in the first row of the resulting matrix.

For the first element, we have 1*1 + 1*3 + 2*0 = 4. This means that the first element in the first row of the resulting matrix will be 4.

We can repeat this process for the remaining elements in the first row and the first column, giving us:

- First row, second column: 1*1 + 1*3 + 2*3 = 10
- Second row, first column: 0*1 + 2*3 + 1*0 = 6
- Second row, second column: 0*1 + 2*3 + 1*3 = 9
- Third row, first column: 1*1 + 0*3 + 3*0 = 1
- Third row, second column: 1*1 + 0*3 + 3*3 = 10

Putting these values into a matrix, we get:

\left(\begin{array}{cc}4&10\\6&9\\1&10\end{array}\right)

I hope this helps clarify the process of matrix multiplication for you. Keep practicing and you'll become more comfortable with it!