Sect' 4'1 Introduction to Matrices

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Sect. 4.1 Introduction to Matrices
Goal 1 Organize Data in Matrices Goal 2
Solve Equation Involving Matrices
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Matrix A matrix is an ordered set of numbers
listed rectangular form.
Example. Let A denote the matrix A
This matrix A has three rows and four columns.
We can name it by its Dimensions. It is a 3 x 4
matrix. We can also name it A 3 x 4
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The aij are called matrix elements.
An         matrix consists of m rows and n
columns
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The Location of an Element We can describe the
location or position within the matrix of any of
the elements in words, by saying which row and
which column it is in. So in the matrix below,
the element "-5" is in the top row, that's row 1
and in column 4.
A
A quicker way to describe its position is to use
subscripts. In matrix A, the element in the first
row and the first column is written as A11. -
In the matrix above, A113. - Element A14 is
-5. - The first subscript refers to the row,
the second to the column.
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Row matrix A matrix with one row is called a row
matrix
Column matrix A matrix with one column is called
a column matrix
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Zero-matrix When all the elements of a matrix A
are 0, we call A a zero-matrix.
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How would you describe this matrix?
                 
This matrix has 3 rows and 5 columns. That means
it's a "3 x 5" matrix.
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Square Matrix In the case when m (number of rows)
is equal to n (number of columns), we say that
the matrix is square.         
This is a square matrix, since m n 3
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Equal matrices For two matrices to be equal,
every single element in the first matrix must be
equal to the corresponding element in the other
matrix.
So these two matrices are equal
These two are not
             This means that if two matrices
are equal, then they must have the same
Dimensions (numbers of rows and columns as each
other). So a 3 x 3 matrix could never be equal
to a 2 x 4 matrix.
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Solve
(5, -4)
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Solve