MATRICES

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## MATRICES

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**MATRICES**A rectangular array of numbers enclosed in a square brackets (or parentheses) is called a matrix (the plural is matrices) The entries of a matrix are called elements.**Example #1**Consider the following two matrices. Is there any difference between them? Yes! M has 3 rows and 2 columns whereas N has 2 rows and 3 columns**Order of a matrix**If a matrix has m rows and n columns, we say that it is a matrix of order m X n, read m by n. We also refer to it as an m X n matrix. The first number (m) refers to the number of rows and the second number (n) to the number of columns.**Example #2**Find the order of each of the following matrices: 2 X 3 1 X 4 3 X 1**Matrix Operations**Now that we know the basic notions about matrices, we next consider how to perform operations with them. Addition We add matrices by adding corresponding elements.**Subtraction**We subtract matrices by subtracting corresponding elements. Remark: To add or subtract matrices, they must have the same order. Multiplication by a number To multiply a matrix by a number, we multiply each element of the matrix by the number.**Example #3**Compute: where The matrices have the same order, so they can be added.**where**Since the matrices have the same order, they can be added.**where**Since the matrices don’t have the same order, we cannot compute their difference.**Equalityof matrices**• Two matrices are equal if • they have the same order and • their corresponding elements are the same**Example #4**Find x and y if :**Example #5**The monthly expenditures (in dollars) for entertainment (E), food (F), and housing (H) per person under 25 and 25-34 years old are as show What would be the annual expenditures in the categories under 25 and 25-34?**To find the annual expenditures, we multiply the given**matrix by 12 (since there are 12 months in a year) and obtain