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Jorge Q.
Researcher and Tutoring experience for over 5 years
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MATLAB
TutorMe
Question:

If $$A$$ and $$B$$ are both $$5\times5$$ matrices defined in MATLAB, what is the difference between the following operations? >> C = A * B; >> C = A.*B

Jorge Q.
Answer:

The first operation is a MATRIX multiplication, which means that $$A$$ and $$B$$ are multiplied by the standard rules of linear algebra, namely $$C=AB$$. The second operation is a POINT-BY-POINT multiplication, which means that each entry of $$A$$ will be multiplied with the matching position entry in $$B$$ and placed in the corresponding point in $$C$$.

Pre-Calculus
TutorMe
Question:

Is the matrix $$A = \begin{bmatrix} 0.5 & -2 \\ -3 & 12 \end{bmatrix}$$ invertible? If so, find $$A^{-1}$$. If not, explain why.

Jorge Q.
Answer:

The matrix $$A$$ is not invertible, since $$det(A)= (0.5)*(12)-(-3)*(-2)=0$$, and a matrix can only be invertible if $$det(A) \neq 0$$

Basic Math
TutorMe
Question:

Five years ago Peter's age was twice as Dinah's. How old will Peter be in two years, if their current ages sum 25?

Jorge Q.
Answer:

If we define Peter's current age as $$P$$ and Dinah's current age as $$D$$, then: Peter's age 5 years ago: $$P-5$$ Dinah's age 5 years ago: $$D-5$$ We know that Peter doubled Dinah's age by then, so: $$P-5=2(D-5) = 2D -10$$ So the relation can be simplyfied to $$P=2D-5$$. Finally, we know that their current ages sum is 25, so: $$P+D=25 \rightarrow P=25-D$$. We now have two different expressions that are equal to $$P$$, so we can do: $$2D-5=25-D \longrightarrow 3D-5=25 \longrightarrow 3D = 30 \longrightarrow D=10$$ So since we know that Dinah is 10 years old, then Peter's age is $$P=25-10=15$$, and his age in two years will be 17.

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