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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.

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.

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.

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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