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 […]

Find a basis for the space of 2×2 lower triangular matrices.

The main objective of this question is to find the basis space for the lower triangular matrices. This question uses the concept of basis space. A set of vectors B is referred to as a basis for a vector space V if each element of V can be expressed as a linear combination of finite […]

Determine if the columns of the matrix form a linearly independent set. Justify each answer.

(begin{bmatrix}1&4&-3&0\-2&-7&4&1\-4&-5&7&5end{bmatrix}) The main objective of this question is to determine whether the columns of the given matrix form a linearly independent or dependent set. If the non-trivial linear combination of vectors equals zero, then the set of vectors is said to be linearly dependent. The vectors are said to be linearly independent if there is […]