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UH / Mathematics / MATH 1313 / How are rows and columns measured in a matrix?

# How are rows and columns measured in a matrix? Description

##### Description: A matrix is a rectangular array of numbers, letters, symbols, or algebraic expressions that are arranged in rows and columns. Capital letters of the English alphabet are typically used to name a matrix
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MATH 1313, Week 3 Notes Don't forget about the age old question of How are the physical quantities of matter measured?

Chapter 3: Matrices

Section 3.1: MatricesWe also discuss several other topics like How to maintain the body temperature?

•A matrix is an ordered rectangular way of numbers, letters, symbols or algebraic expressions. A matrix with m rows and n columns has size or dimension m  nIf you want to learn more check out What are the benefits of studying Archaeology?

•The real numbers that make up the matrix are called entries or elements of the matrix.If you want to learn more check out Where did cash come from?

•The entry in the ith row and jth column is dense by a i j

If you want to learn more check out colonies towson

•A matrix with only one column or one row is called a column matrix (or  column vector) or row matrix (a now vector), respectivelyIf you want to learn more check out the goophered grapevine summary

Ex. 1: Diven A=        2     7      7       1

-5     3       9       2

0    -10    20      3

1    -3     -11      4

A. What is the dimension of A? Rows x columns

B. Identify a4 3.                        4th row, 3rd column =

•Systems of Linear Equations in Matrix Form

-In order to write a system of linear equations in matrix form, first make sure the like variables occur in the same column.

❋Then we’ll leave out the variables of the system and simply use the coefficients and constants to write the matrix form.

-Diven the following system of equations:

2x+4y+6z=22

3x+8y+5z=27

-x+y+2z=2                x     y     z

-The coefficient matrix is:        2    4     6

3    8     5

-1   1     2

-The constant matrix is:     22

Equal to               27

Put                        2

-The augmented matrix is:        x     y     z

2    4     6            22

3    8     5            27

-1   1     2        2

Ex. 2: Dive the coefficient, constant and augmented matrix for the system of equations.

2x-4y=15

-3y+2z=9

x+y-32=-8

Coefficient Matrix=   2       -4      0

0       -3      2

1               1      -3

Constant Matrix:         15

9

-8

Augmented Matrix:         2      -4    0      15

0      -3    2       9

1       1   -3        -8

Section 3.2: Solving Systems of Linear Equations Using Matrices

•As you may recall from college algebra or section 1.3, you can solve a system of linear equations in two variables easily by applying the substitution or addition method.

-since these methods become tedious when solving a large system of equations,

A suitable technique for solving such systems of linear equations will consist of

Row Operations.

-the sequence of operations on a system of linear equations are referred to equivalent

Systems, which have the same solution set.

•Row Operations

1. Interchange any two rows. swap

1   -1   3                                1   3   5

1    3    5            R1 ↔ R2                 2  -1   3

1. Replace any row by a nonzero constant multiple of itself.        Create 1’s

2   -1   3        R2 →R2                2   -1   3

4   -2   8                                1  -    2

1. Replace any row by the sum of that row and a constant multiple of any other row.         Create a O

1   3   5        -2R1+R2→R2                1   3   5

2  -1   3                                0  -7  -7

-2(1  3  5) →  -2  -6  -10

+2  -1   3_

0  -7  -7

New R2

•Row Reduced Form

-An mxn augmented matrix is in row-reduced form if it satisfies the following conditions:

1. Each row consisting entirely of zeros lies below any other row having nonzero entries.

1   0   -3                R2 ↔ R3                   1   0   -3

0   0    0        the correct non-reduced form    0   1   -2

0   1   -2                                            0   0    0

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