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1 answer:
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For any arbitrary 2x2 matrices 
and 
, only one choice of exists to satisfy 
, which is the identity matrix.
There is no other matrix that would work unless we place some more restrictions on. One such restriction would be to ensure that is not singular, or its determinant is non-zero. Then this matrix has an inverse, and taking 
we'd get equality.
There is no other matrix that would work unless we place some more restrictions on
Answer:
a) The slope of the function is 3.
c) The equation is represented by .
d) The y-intercept of the function is 35.
Step-by-step explanation:
a) According to the statement, we must assume that number of pieces of mail that must be hand-sorted (dependent variable) is represented by a linear function in terms of time (independent variable). That is:
(1)
Where:
- Slope, measured in number of pieces per minute.
- Time, measured in minutes.
- Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.
- Current number of pieces of mail that must be hand-sorted, measured in pieces.
From Geometry, we know that a line can be formed by know two distinct points. If we know that and
, then the following system of linear equations is formed:
(2)
(3)
The solution of the system of equations is:
and
The slope of the function is 3.
c) By (1) and using results from a) we conclude that the equation function is:
(4)
d) The y-intercept of the function is 35.