Matrices Flashcards
# define: matrix
A
- *rectangular arrangement** of
- *numbers** into
- *rows and columns**.
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In plainspeak,
what is a
matrix?
A
compact representation of numbers.
What are the
dimensions
of matrix B?
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3 x 2
Pronounced “three by two.”
Rows x Columns
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- *Envision** a
- *2 x 3 matrix**.
Rows x Columns
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What is
- *another word** for a
- *matrix entry**?
Matrix element
How could you
- *identify** the
- *entry −7** in
- *matrix G**?
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g1,3
It’s the entry in the first row and the third column.
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What is
element g2,1?
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18
It’s in the second row and the first column.
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# _define_: augmented matrix
A matrix that
- *represents** a
- *system of equations**.
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In an
augmented matrix,
what does each
row represent?
One equation
in the system of equations
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In an
augmented matrix,
what does each
column represent?
A
variable
or the
constant terms
in the system of equations
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- *Envision** the
- *augmented matrix** that
- *represents** the
- *system below**.
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- *Envision** the
- *augmented matrix** that
- *represents** the
- *system below**.
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- *Envision** the
- *augmented matrix** that
- *represents** the
- *system below**.
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What are the
- *three** elementary
- *matrix row operations**?
Switch any two rows
Add one row to another
Multiply a row by a
nonzero constant
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Why can you
switch any two rows in an
augmented matrix?
The
- *order** of the equations
- *doesn’t matter**.
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Why can you
add one row to another in an
augmented matrix?
Because you can
- *add two equal quantities** to
- *both sides** of an equation.
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Why can you
multiply a row by a nonzero constant in an
augmented matrix?
Because you can
- *multiply both sides** of an equation by the
- *same nonzero constant**.
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How do you
- *notate**
- *interchanging rows 1 and 2**?
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How do you
- *notate**
- *multiplying row 2 by three**?
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How do you
- *notate**
- *replacing row 2** with the
- *sum of rows 1 and 2**?
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Just add the corresponding entries.
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Just subtract the corresponding entries.
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Undefined
Cannot add or subtract matrices with different dimensions.
When working with
matrices,
how do you
refer to
real numbers?
Scalars
Any real number that is
not a part of the matrix is a
scalar.
# _define_: matrix equation
An
- *equation** in which the
- *variable** stands for a
- *matrix**.
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# _define_: zero matrix
A
- *matrix** in which
- *all entries are 0**.
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When working with
matrices,
what does
O mean?
A zero matrix
What are the
dimensions of the
zero matrix in the equation
B + O = B
given that:
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2 x 3
If the dimensions of a zero matrix aren’t given, it’s understood that the dimensions match the dimensions of matrix B.
How would you
notate a
zero matrix with
two rows and four columns?
O2x4
A zero matrix is indicated by O,
and a subscript can be added to indicate the dimensions of the matrix if necessary.
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Given
matrices A and O,
A − O = _____?
A
When we add the
m x n zero matrix to
any m x n matrix A, we get
matrix A back.
Given
matrix A,
A + −A = _____?
O