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Simple Equations

Review Answers and are two solutions. The intercepts are located at and We have a linear relationship between and so its graph can be sketched as the line passing through any two solutions. by solving for we have so two solutions are and The intercepts are located at and the intercept is located at The graph is symmetric in the axis. Using your graphing calculator, enter the relationship on the Y= menu. Viewing a table of points, we see many solutions, say and and the intercepts at and By inspection we see that the graph is symmetric about the origin.

CK-12 Foundation (2010-09-10). CK-12 Calculus (Kindle Locations 94-103). CK-12 Foundation. Kindle Edition.

 
. Note that both matrices being added are 2×3, and the resulting matrix is also 2×3. You cannot add two matrices that have different dimensions.

As you might guess, subtracting works much the same way, except that you subtract instead of adding.





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Once again, note that the resulting matrix has the same dimensions as the originals, and that you cannot subtract two matrices that have different dimensions.

Multiplying a Matrix by a Constant

What does it mean to multiply a number by 3? It means you add the number to itself 3 times.

Multiplying a matrix by 3 means the same thing…you add the matrix to itself 3 times.


3


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+

+

=

Note what has happened: each element in the original matrix has been multiplied by 3. Hence, we arrive at the method for multiplying a matrix by a constant: you multiply each element by that constant. The resulting matrix has the same dimensions as the original.




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