Suppose you are an algebra teacher grading the following solution on an examination: − 3 ( x − 6 ) = 2 − x − 3 x − 18 = 2 − x − 2 x − 18 = 2 − 2 x = − 16 x = 8 You should note that 8 checks, so the solution set is (8). The student who worked the problem therefore wants full credit. Can you find any errors in the solution? If full credit is 10 points, how many points should you give the student? Justify your position.
Suppose you are an algebra teacher grading the following solution on an examination: − 3 ( x − 6 ) = 2 − x − 3 x − 18 = 2 − x − 2 x − 18 = 2 − 2 x = − 16 x = 8 You should note that 8 checks, so the solution set is (8). The student who worked the problem therefore wants full credit. Can you find any errors in the solution? If full credit is 10 points, how many points should you give the student? Justify your position.
Solution Summary: The author explains that the student's final answer is correct, but the steps in the question are wrong.
Suppose you are an algebra teacher grading the following solution on an examination:
−
3
(
x
−
6
)
=
2
−
x
−
3
x
−
18
=
2
−
x
−
2
x
−
18
=
2
−
2
x
=
−
16
x
=
8
You should note that 8 checks, so the solution set is (8). The student who worked the problem therefore wants full credit. Can you find any errors in the solution? If full credit is 10 points, how many points should you give the student? Justify your position.
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ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0.
y Af
-2
1
2 4x
a. The function is increasing when
and
decreasing when
By forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1
if a=2 and b=1
1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2
2)Find a matrix C such that (B − 2C)-1=A
3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)
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