Finding Standard Matrices for Compositions In Exercises 47 and 48, find the standard matrices for T = T 2 T 1 and T ′ = T 1 T 2 . T 1 : R 2 → R 3 , T 1 ( x , y ) = ( x , x + y , y ) T 2 : R 3 → R 2 , T 2 ( x , y , z ) = ( 0 , y )
Finding Standard Matrices for Compositions In Exercises 47 and 48, find the standard matrices for T = T 2 T 1 and T ′ = T 1 T 2 . T 1 : R 2 → R 3 , T 1 ( x , y ) = ( x , x + y , y ) T 2 : R 3 → R 2 , T 2 ( x , y , z ) = ( 0 , y )
Solution Summary: The author explains that the standard matrices for T=T_1 and tprime are left[cc0
M = log
The formula
determines the magnitude of an earthquake,
where / is the intensity of the earthquake and S is the intensity of
a "standard earthquake." How many times stronger is an
earthquake with a magnitude of 8 than an earthquake with a
magnitude of 6? Show your work.
Now consider equations of the form ×-a=v
= √bx + c, where a, b, and c
are all positive integers and b>1.
(f) Create an equation of this form that has 7 as a solution and
an extraneous solution. Give the extraneous solution.
(g)
What must be true about the value of bx + c to ensure that
there is a real number solution to the equation? Explain.
The equation ×+ 2 = √3x+10 is of the form ×+ a = √bx + c, where a, b, and
c are all positive integers and b > 1. Using this equation as a
model, create your own equation that has extraneous solutions.
(d) Using trial and error with numbers for a, b, and c, create an
equation of the form x + a = √bx + c, where a, b, and c are all
positive integers and b>1 such that 7 is a solution and there
is an extraneous solution. (Hint: Substitute 7 for x, and
choose a value for a. Then square both sides so you can
choose a, b, and c that will make the equation true.)
(e) Solve the equation you created in Part 2a.
Chapter 6 Solutions
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