The Lin family bought a dozen bagels. They ate 1/4 of the bagels today and 5/12 of the bagels yesterday. What fraction of the ba
gels did they eat in all? Explain how you found your answer.
1 answer:
Answer:
2/3
Step-by-step explanation:
To be able to find what the total fraction of bagels eaten, the fractions need to have common denominators. To do this, you multiply 1/4 by 3 in both the numerator and the denominator. Now that the two fractions have the same denominator, you can add the fraction's numerator to get the total fraction, 8/12. However, 8/12 can be simplified more, so you divide by 4 and end up with 2/3.
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Answer: The required answers are
(a) T is proved to be a linear transformation.
(b) The matrix A such that T(x) = Ax is
Step-by-step explanation: We are given a linear transformation T : R³ → R² defined as follows :
We are to
(a) prove that T is a linear transformation
and
(b) find a matrix A such that T(x) = Ax.
(a) Let s, t are any real numbers and (a, b, c), (a', b', c') ∈ R³.
Then, we have
So, we get
Therefore, T is a linear transformation.
(b) We know that B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} is a standard basis for R³ and B' = {(1, 0), (0, 1)} is a standard basis for R².
So, we have
So, the matrix A such that T(x) = Ax will be given by
Thus,
(a) T is proved to be a linear transformation.
(b) The matrix A such that T(x) = Ax is