Question

answer all steps, please

2. Let A8 28 -4 -6 13 a) Compute l|All (Frobenius norm), |Alo and ||Alli (by hand b) Compute A-1 and the norms l|All2 and IA12 in MATLAB. c Use MATLAB to compute the condition nmber in norm-2 of A, based on your results from (b). Verify your results in MATLAB using the cond command

Answer 1

IF YOU HAVE ANY DOUBTS COMMENT BELOW I WILL BE THERE TO HELP YOU ALL THE BEST

AS FOR GIVEN DATA...

a) Compute ||Alls (Frobenius norm).All and ||Alli (by hand

SOL ::-)The Forbenius norm is

||A||_Fr =

=( |2|² + |2|² + |1|² + |8|² + |2|² + |8|² + |-4|² + |-6|² + |13|² )^½

^{=(4+4+1+64+4+64+16+36+169)^1/2}

⁼(362)^½

^=19.026

The -norm is
||A|| = | a_ij | , the maximum of the row sums
= max{ |2| + |2| + |1|, |8| + |2| + |8|, |-4| + |-6| + |13| } = max{ 5,18,23 } = 23

The 1-norm is
||A||₁ = | a_ij | ,   the maximum of the column sums

= max{ |2| + |8| + |-4|, |2| + |2| + |-6|, |1| + |8| + |13| } = max{ 14, 10, 22 } = 22

b) Compute A and the norms ||All2 and |A

SOL ::-

for inverse of matrixA

A=[2 2 1;8 2 8;-4 -6 13]

X=inv(A)

For norm-2

n=norm(A)

For norm-2 of inverse of matrix A

A=inv(sym(magic(3)))

norm2=norm(A)

c) Use MATLAB to compute the condition number in norm-2 of A, based on your results 112 in MATLAB. from ). Verify your results in MATLAB using the cond command

SOL ::-

for computing the 2-norm condition number of the inverse of the matrix A

A=inv(sym(magic(3)));

condN2=cond(A)

I HOPE YOU UNDERSSTAND..

PLS ..RATE THUMBSUP IT HELPS ME ALOT

THANKS GOODLUCK

THANK YOU....!