This question aims to understand the construction of a matrix under given constraints. To solve this question, we need to have a clear understanding of the terms column space and null space. The space which is spanned by the column vectors of a given matrix is called its column space. Read moreDetermine if the columns […]
Category Archives: Matrices Q&A
This problem aims to get us familiar with vector solutions. To better understand this problem, you should know about the homogeneous equations, parametric forms, and the span of vectors. We can define parametric form such that in a homogeneous equation there are $m$ free variables, then the solution set can be represented as the span of […]
[ A = begin{bmatrix} 1 & -2 & 5 & 6 \ 5 & 1 & -10 & 15 \ 1 & -2 & 8 & 4 end{bmatrix} ] This question aims to find the null space which represents the set of all solutions to the homogeneous equation and column space which represents the range of a […]
[ 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 […]
A row replacement operation does not affect the determinant of a matrix. The determinant of $A$ is the product of the pivots in any echelon form $U$ of $A$, multiplied by $(-1)^r$, where $r$ is the number of row interchanges made during row reduction from $A$ to $U$. If the columns of $A$ are linearly […]