(a) Write down the definition of the inverse of an n × n matrix A. (b)...
The inverse of a square matrix A is denoted A-1 , such that A × A-1 = I, where I is the identity matrix with all 1s on the diagonal and 0 on all other cells. The inverse of a 2×2 matrix A can be obtained using the following formula: = c d a b A − − − = − c a d b ad bc A 1...
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforward Gauss (or Jordan) elimination (Problem 7 is a particular case for n 3). First you write down the augmented matrix A and apply the Gauss process to this as discussed in class: A-la2,1 a2,2 a2,n : an,1 an,2 .. an.n 0 0 1 3. Derive the Jordan elimination algorithm without pivoting for the augmented matrix in terms of a triple...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pivoting to find an upper triangular matrix U, permutation matrices Pi and P2 and lower triangular matrices Mi and M2 of the form 1 0 0 Mi-1A1 10 a2 0 1 M2 0 0 0 b1 with ail...
2. Inverse of a square matrix: Determine the inverse matrix [A™'] of the given square matrix [A] using the Gauss-Jordan Elimination Method (GEM), and verify that [A-!] [A] = I where I is the identity matrix. A = [ 1 4 -27 0 -3 -2 | -3 4 1
ALTSIS AND NUMERICAL ANALYSIS 2. (a) Let A be the matrix 2 -115 8-4 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P Use Gaussian elimination with partial pivoting to find an upper triangular matix U, permutation matrices Pi and P2 and lower triangular matrices M and M2 of the form 1 0 0 0 1 1 0 0 0 bi 1 with land...
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT. Give a proof that if A has an inverse, then so does AT. (c) Let A be a 3 x 3 matrix that can be transformed into the identity matrix by perform ing the following three row operations in the given order: R2 x 3, Ri R3, R3+2R1 (i) Write down the elementary...
Exercise 1. (a) Find the inverse of the matrix 0 0 1/2 A= 01/ 31 1/5 1 0 (b) Let N be a nxn matrix with N2 = 0. Show (I. - N)-1 = IA+N. (Hint: Use the definition of the inverse.)
Pr. 2 Consider the Beam Matrix formulation presented in class. Use the definition of Matrix Inverse to find the inverse of the "Lambda Matrix" for a beam finite element given below: (show the work by hand in detail) [41-1 [1 0 0 0 1 0 1 L 12 Lo 1 2L 0 0 L3 3L = T? ? ? ? ? ? ? ? ? ? ? ? L? ? ? ?] Once you find the [A] 4, then you...
1. Write a MATLAB function that takes a matrix, a row number and
a scalar as
arguments and multiplies each element of the row of the matrix by
the scalar returning the
updated matrix.
2. Write a MATLAB function that takes a matrix, two row numbers and
a scalar as
arguments and returns a matrix with a linear combination of the
rows. For example, if the rows
passed to the function were i and j and the scalar was m,...
write an 8051 assembly program to find the inverse of matrix (3x3) and save the inverse matrix in 430h ORG 400H MATRIXA1: DB 4,6,9,1,9,3,0,2,.5
write an 8051 assembly program to find the inverse of matrix (3x3) and save the inverse matrix in 430h
ORG 400H MATRIXA1: DB 4,6,9,1,9,3,0,2,.5