What are scalars and vectors in linear algebra? A scalar in linear algebra is a single number that can scale or stretch a vector or matrix. For example, 1, 2.3, -4, etc. are scalars. On the other hand, a vector in linear agebra is a list of numbers. The number of...

How to perform matrix scalar multiplication? Let’s say A is a matrix with the following elements. $latex A={\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}} $ And λ = 3 is a scalar. If we multiply A and λ, we will get another matrix B such that: $latex B=\lambda...

What is the transpose of a matrix? Let’s say A is a matrix that has 2 rows and 3 columns. $latex A={\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}} $ Let’s also say that B is the transpose of matrix A. $latex B=A^T $ In linear algebra, the transpose of a matrix...

Let’s say A and B are two mxn matrices. We can add these two matrices and get another matrix C. If the element of ith row and jth column of the matrix A, B, and C are Ai,j, Bi,j, and Ci,j, respectively, then we can say: $latex C_{i,j}=A_{i,j}+B_{i,j} $ Let’s look at...