Tutor profile: Geetanshu C.
Subject: Linear Algebra
Basic Question : Give the order of following matrix: [ -1 4 8 -6]
We all know what a row and a column means. Order of a matrix means No. of rows(Nr) * No. of columns(Nc) Here we are having 4 elements but in a single row Thus , Nr= 1 4 elements are corresponding to 4 columns. Thus, Nc= 4 Order = 1 * 4
The area of a right triangle is 200. One of its angles is 45 degree. Find the lengths of sides and hypotenuse of triangle.
Firstly, do we know formula for area of a triangle? Yes, it is (1/2)*base*height where height means altitude or perpendicular distance of top from base. Since, it is a right triangle, one angle is 90 degree. Other angle is given as 45 degree. We know that sum of angles of a triangle is 180 degree. Thus, x + 45 + 90 = 180 where x is third angle. So, x=45 Since both angles are equal, sides opposite to them must also be equal. This implies that base= height= L Area = 200= (1/2)*L*L Thus, L=20(Answer) Sin(45)=Perpendicular/Hypotenuse Thus, Hypotenuse=Perpendicular*root(2) Sin(45)=1/root(2) = 20*root(2)
If x is less than 3, simplify: mod(x-3)-5*mod(-6).
We are given that x is less than 3, so we can say that (x-3) will be a negative number. And we know mod means magnitude or only positive value. So to get mod(x-3), we can write it as -(x-3) as this will be the magnitude(or positive value) Similarly mod(-6) gives us value as 6(magnitude only) Now substituting the values, we have: -(x-3)-5*(6) = -x+3-30 = -x-27 (Answer)
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