Unit+4+-+Matrices

__**Unit 4-MATRICES**__
__//**Big ideas:**//__ Dimensions entries is number of rows by number of columns. For example a 2X2 matrix means that there are 2 rows and 2 columns.

Matrices can only be added or subtracted when the matrices have the same dimensions. A 2X3 matrix cannot be multiplied by a 4X3 matrix, but a 2X3 matrix can be multiplied by a 2X3 matrix.

Multiplying matrices is different than adding or subtracting matrices. You can only multiply two matrices when the number of columns in the first matrix is the same as the number of rows in the second matrix. For example, multiplying a 2X3 matrix and a 3X2 matrix would work; but, however, multiplying a 2X3 matrix by a 2X2 matrix would not work.

When you multiply the numbers in the matrix you will get several different numbers. to get the final answer for a certain row or column, you add together all the products of the numbers you multiply. The product of matrix multiplication should result in a matrix that has the same number of rows as the first matrix and the same number of columns as the second matrix. For example if you were to multiply a 2X3 matrix by a 3X1 matrix, it would result in a 2X1 matrix.

Matrices might seem pretty useless, but they can be used in real world problems such as finding the total cost for supplies for a sports team. The following matrix is an example of such a problem. Key= B= bats, Ba=balls, U=uniforms. ---B--Ba-U...........Cost of items Women team[ 12 45 15 ] x [21] Men team [ 15 38 17 ] '[4 ] [30]

The result of these two matrices being multiplied should be [882] .....................................................................................[977] I'll show what i did to get to this conclusion. multiply first row by first column(which is the only column in this case) which would result in these numbers: 252, 180, and 450. Then add them, which gets you 882. this is the first number in your matrix product, which will be a 2X1. The next row will get multiplied by the column as well which gets 315, 152,510. Adding them gets you 977 which gets you your next number in the 2X1 matrix.

__** Vocab **__

__Matrix-__ A rectangular arrangement of numbers in rows and columns. __Dimensions-__ Number of rows by numbr4 of columns. __Entries-__ The number in a matrix. __Scalar-__ A number that is multiplied by all elements of a matrix. __Multiplying Matrices-__ The number of columns in the first matrix must be equal to the number of rows in the second matrix.

Here is a video to help with learning how to do a matrix step-by-step. []