Give atleast 3 examples of each type of matrix. I. Idempotent Matrix
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- Do all mxn matrix has a determinant?Type in Latex **Problem**. Let $$A = \begin{bmatrix} .5 & .2 & .3 \\ .3 & .8 & .3 \\ .2 & 0 & .4 \end{bmatrix}.$$ This matrix is an example of a **stochastic matrix**: its column sums are all equal to 1. The vectors $$\mathbf{v}_1 = \begin{bmatrix} .3 \\ .6 \\ .1 \end{bmatrix}, \mathbf{v}_2 = \begin{bmatrix} 1 \\ -3 \\ 2 \end{bmatrix}, \mathbf{v}_3 = \begin{bmatrix} -1 \\ 0 \\ 1\end{bmatrix}$$ are all eigenvectors of $A$. * Compute $\left[\begin{array}{rrr} 1 & 1 & 1 \end{array}\right]\cdot\mathbf{x}_0$ and deduce that $c_1 = 1$.* Finally, let $\mathbf{x}_k = A^k \mathbf{x}_0$. Show that $\mathbf{x}_k \longrightarrow \mathbf{v}_1$ as $k$ goes to infinity. (The vector $\mathbf{v}_1$ is called a **steady-state vector** for $A.$) **Solution**. To prove that $c_1 = 1$, we first left-multiply both sides of the above equation by $[1 \, 1\, 1]$ and then simplify both sides:$$\begin{aligned}[1 \, 1\, 1]\mathbf{x}_0 &= [1 \, 1\, 1](c_1\mathbf{v}_1 +…Write a code to check multiplicability of a matrix.
- construct a Playfair matrix with the key "largest"Given a 2-D square matrix: ant mat{3}[{3]={{1, 2 3} {4,586}, {7.8.9FF Write a function transpose which Create a 3*3 matrix trans and store the transpose of given matrix in it.And prxnt the ' transpose, IN C++.I have seen the library so please dont send me it Show that any two rows of a matrix can be interchanged by elementary rowtransformations of the other two types (i.e. , of the type Ri → kRi and Rj → Rj +kRi).
- How does duality play a role in linear algebra, particularly in matrix operations?What is the worst-case running time complexity of matrix substraction? select one: a.O(n^2.5) b.O(2n) c.O(n^2) d.O(3^n)Let M, represent the matrix representation of a certain relation R on the set A. Consider a set A with n distinct elements. M, would therefore be a n x n matrix. How many 1s and 0s will M contain if R is a rooted (directed) tree?