### Assume that A is row equivalent to B. Find bases for Nul A and Col A.

[ A = begin{bmatrix} 4 & -3 & -17 & 27 \ 2 & 3 & 5 & -9 \ -8 & -9 & -11 & 21 end{bmatrix} ] [ B = begin{bmatrix} 1 & 0 & -2 & 3 \ 0 & 1 & 3 & -5 \ 0 & -15 & -45 & […]

### Use coordinate vectors to test the linear independence of the sets of polynomials. Explain your work.

[ 1 + 2t^3, 2 + t – 3t^2, -t + 2t^2 – t^3] This problem aims to familiarize us with vector equations, linear independence of a vector, and echelon form. The concepts required to solve this problem are related to basic matrices, which include linear independence, augmented vectors, and row-reduced forms. To define linear […]

### At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of $40$ freshmen sharing a common lounge area.

How many international students would you expect to find in a typical cluster? With what standard deviation? This question aims to find the expected number of international students in a typical cluster along with their standard deviation. Take into consideration what a random variable is: a collection of numerical values resulting from a random process. […]

### Find x such that the matrix is equal to its own inverse.

[ M=left[ begin{matrix}7&x\-8&-7\end{matrix} right]] The aim of the article is to find the value of the variable $x$ within the given matrix for which it will be equal to its inverse matrix. The basic concept behind this question is the understanding of the Matrix, how to find the determinant of a matrix, and the inverse […]

### Determine the head of the vector whose tail is given. Make a sketch.

– Given vector [ left[begin{matrix}-2\5\end{matrix}right] ] – Tail of the vector is $( -3, 2)$ [ left[begin{matrix}-3\2\end{matrix}right] ] In this question, we have to find the head of the vector when the vector and its tail are given. The basic concept behind this question is the knowledge of vectors, subtraction addition, and multiplication of […]