I skipped algebra I so I never learned about matrices. If you had a 2X3 matrix & multiplied it by a 3X2 matrix, what size would the product matrix be? Would it be a 3X3? Is there any way to know? I have a test monday and i want to make sure I know this.
To determine the size of the product matrix of two matrices, you need to understand the rules of matrix multiplication.
In general, if you have an m x n matrix multiplied by an n x p matrix, the product matrix will be of size m x p.
In your case, you have a 2 x 3 matrix multiplied by a 3 x 2 matrix. Following the rule mentioned above, the product matrix would be of size 2 x 2, not 3 x 3.
So, for your specific situation, the product matrix would be of size 2 x 2.
It's important to note that the number of columns in the first matrix should be equal to the number of rows in the second matrix to carry out matrix multiplication.
To determine the size of the product matrix when multiplying two matrices, you need to follow a specific rule:
For example, if you have a matrix A with dimensions m x n, and another matrix B with dimensions n x p, then the resulting product matrix AB will have dimensions m x p.
In your case, you have a 2x3 matrix multiplied by a 3x2 matrix. According to the rule, the product matrix dimensions will be 2x2, not 3x3. The number of columns in the first matrix (3) matches the number of rows in the second matrix (3), so the resulting matrix will have the remaining dimensions, 2x2.
Remember, when multiplying matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix for the multiplication to be possible.
Now, for your upcoming test, it is recommended to practice by doing some matrix multiplication problems to reinforce the concepts. This will help you become more familiar with the rules of matrix multiplication, and you will be better prepared to tackle similar questions on your test.