mxn matrix B. Show that if A is the standard matrix for T, then A= B. [Hint: Show that A and B have the same columns.] transformation Tonto

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. The determinant of an n X n matrix can be used in solving systems of linear equations, as well as for other purposes. The determinant of A can be defined in terms of minors and cofactors. The minor of element aj is the determinant of the (n – 1) X (n – 1) matrix obtained from A by crossing out the elements in row i and column j; denote this minor by Mj. The cofactor of element aj, denoted by Cj. is defined by Cy = (-1y**Mg The determinant of A is computed by multiplying all the elements in some fixed row of A by their respective cofactors and summing the results. For example, if the first row is used, then the determi- nant of A is given by Σ (α(CI) k=1 Write a program that, when given n and the entries in an n Xn array A as input, computes the deter- minant of A. Use a recursive algorithm.

Problem 5. Let u = g – g(-), where g-) = (g-1, 90, 91,...,gr-1). Interpret the physical meaning of the vector u.

Change of Basis for a Linear Transformation Write a function called vecTransform that receives a two-dimensional vector, v defined with respect to the standard Cartesian basis, and then returns a transformed vector W = T() that is twice as long as and is mirrored about the line line 3y + x = 0 Function > 1 T(V) 1 % Test vector v 2 v= [10]; 3 Code to call your function > 3y + x = 0 4% Perform Transform 5 W vecTransform(v) Save My Solutions > C Reset MATLAB Documentation C Reset

Manula solution

How do you express a system of linear equations as a single matrix-vector equation of the form Ax=b? Demonstrate the conversion process clearly using examples for each step.

Use a simple algorithm to do the following ant it as a matlab code 1. Determine the mean of the elements of a matrix A WITHOUT using the mean function 2. Find out how many non-zero elements a matrix A has 3. Sum the diagonal elements of a square matrix A 4. Add the first and last elements of a vector v if you are not given the length of v

Use a matlab code

Pls Use Python If there is a non-singular matrix P such as        P-1AP=D  , matrix A is called a diagonalizable matrix. A, n x n square matrix is ​​diagonalizable if and only if matrix A has n linearly independent eigenvectors. In this case, the diagonal elements of the diagonal matrix D are the eigenvalues ​​of the matrix A.   A=({{1, -1, -1}, {1, 3, 1}, {-3, 1, -1}}) : 1 -1 -1 1 3 1 -3 1 -1     a)Write a program that calculates the eigenvalues ​​and eigenvectors of matrix A using NumPy.   b)Write the program that determines whether the D matrix is ​​diagonal by calculating the D matrix, using NumPy. Ps: Please also explain step by step with " # "