Answer all the questions below and press submit to see how many you got right.
Equation : An equation is a mathematical statement in which two expressions are written with an equal sign in between. A solution of an equation is a set of variables that makes the statement a true statement.
Solution : A solution to an equation is a choice of variables that when substituted into the equation results in a true statement.
Square root : The square root of x denoted by √x is the positive number such that (√x)2=√x⋅√x=x. For example √9=3.
Squared : x squared refers to the number x2=x⋅x. For example 3 squared equals 9.
The solutions of the equation x2+px+q=0 are given by the formula: x=−p2±√p24−q. Use this formula to calculate the biggest solution of the equation x2−7x+12=0.
Linear combination : A linear combination of vectors x1,x2,…,xn in a vector space is any vector of the form λ1x1+λ2x2+…+λnxn where λ1,λ2,…,λn are real numbers.
Linear independence : Vectors x1,x2,…,xn in a vector space are called linearly independent if λ1x1+λ2x2+…+λnxn=0 implies λ1=λ2=…=λn=0. In other words vectors are linearly independent if the only linear combination of the zero vector is the trivial one in which all coefficients are zero.
Vector : Most commonly vector refers to a matrix with one column (x1⋮xn). In general a vector is an element of a vector space.
Which of the following vectors are linearly independent of (316) and (1−12)?
Binomial coefficient : A binomial coefficient \binom{n}{k} is defined as \frac{n!}{k!(n-k)!} and equals the number of different sets of k objects one can pick out of n objects.
Factorial : The factorial of a positive integer n written as n! is defined by n!=1\cdot2\cdot3\ldots\cdot n. For example we have 5!=1\cdot2\cdot3\cdot4\cdot 5=120. n! is the number of different permutations of n objects.
\binom{6}{4}=?