 ### 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. Read moreDetermine if […]

### 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. Read moreDetermine if the columns of the matrix form a linearly independent set. Justify each answer.The basic concept behind this question is the […]

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

– Given vector [ left[begin{matrix}-2\5\end{matrix}right] ] Read moreDetermine if the columns of the matrix form a linearly independent set. Justify each answer.– 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. Read […]