Matrix A has dimension m x n and Matrix B has dimension s x t. Design conditions for m, n, s and t so that both matrix products AB and BA are defined.
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Matrix A has dimension m x n and Matrix B has dimension s x t. Design conditions for m, n,
s and t so that both matrix products AB and BA are defined.
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- Problem 1) Change the diagonal elements of a 3X3 matrix to 1. Diagonal elements of the example matrix shown here are 10, 8, 2 10 -4 0 7 8 3 0 0 2 Read the given values from input (cin) using for loops and then write your code to solve the diagonal.Using Matlab, A=[1 2 3;4 5 6;7 8 10]; a)Create a vector version of the original matrix A. b)Extract those entries of the original matrix A that are greater than 5Construct a Matrix form using Matlab from the given equation: A + B + 2C = 1 2A − B + D = −2 A − B − C − 2D = 4 2A − B + 2C − D = 0 Compute the following variables A, B, C & D.
- Draw the following graph as represented in the adjacency matrix below. a b c d A 1 1 1 0 B 0 1 1 0 C 0 0 1 1 d 0 0 0 1If a matrix A has size 5x6 and a matrix B has a size 6x4, then what will be the size of a matrix A*B?Use Excel VBA to write a code for Gaussian Elimination and Newton 's Raphson Method Implement a dynamic sizing that works for any matrix size or system of equations.
- computer graphic Figure shows the matrix M for a 2D transformation. M is made up of two (2) fundamental transformations (i.e. translation, rotation, scaling). Identify the basic transformations that make up M, and their specific parameters.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 +…Consider a 3×3 matrix M. Which of the following statements about M is false.1) M does not need to be diagonal to represent rotations.2) M can be a part of a homogeneous transformation.3) M can represent rotations.4) M can represent at most only one planar rotation. Consider the matrix D = [ e g 0 ] I f a b I [ 0 c d ] Which of the following should be true in orderfor D to represent a rotation about the x-axis of the coordinate system?1) f = g = 0, e = 1, a = −d, b = c.2) e = f = g = 0, a = −d, b = c.3) f = g = 0, e = 1, a = d, b = −c.4) e = f = 0, g = 1, a = d, b = c.
- Consider the chain of matrices below. M = M1 x M2 x M3 x M4 [15 x 5] [5 x 25] [25 x 30] [30 x 45] (a) Show the complete table used by the dynamic programming algorithm for the matrix chain problem.MATLAB Exercise: 1. Generate a 1 x 3 matrix whose entries are the coefficients of the polynomial N(s) = 2s2 + 3s - 1 2. Generate a 1 x 4 matrix whose entries are the coefficients of the polynomial D(s) = s3 +6s2 + 11s - 6 3. Determine the convolution of N(s) and D(s)show the sub problems based on the matrix chain multiplication for A x B x C x D