please i need this in 30 mins all the matrices written are 2x2 colon next line 1 the sets of mat

Name: please i need this in 30 mins all the matrices written are 2x2 colon next line 1 the sets of matrices b 1 2 0 0 1 0 0 2 1 0 2 0 1 0 0 1 bs 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 form bases for the 31989
Uploaded: 2023-06-20T22:52:16-08:00
Duration: 3 min 43 s
Channel: Madhur L
Description: please i need this in 30 mins all the matrices written are 2x2 colon next line 1 the sets of matrices b 1 2 0 0 1 0 0 2 1 0 2 0 1 0 0 1 bs 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 form bases for the 31989

First, we need to verify that B and Bs are indeed bases for the vector space 𝑀2x2(R). To do this

Question

The sets of matrices B = { |1 2 ; 0 0| , |1 0 ; 0 2| , |1 0 ;2 0| , |1 0 ; 0 1| } , Bs = { |1 0 ; 0 0| , |0 1 ; 0 0| , |0 0 ;1 0| , |0 0 ; 0 1| } form bases for the vector space 𝑀2x2(R) of 2 × 2 matrices with real number entries. Give the coordinate vector for [v]B , where v = |9/2 4 ; 1 3| and determine the change of coordinate matrix 𝑃BS<---B .

          The sets of matrices
B = { |1 2 ; 0 0| , |1 0 ; 0 2| , |1
0 ;2 0| , |1 0 ; 0 1| }     ,
Bs = { |1 0 ; 0
0| , |0 1 ; 0 0| , |0 0 ;1 0|
, |0 0 ; 0 1| }
form bases for the vector space 𝑀2x2(R) of 2 × 2
matrices with real number entries. Give the coordinate vector for
[v]B , where v = |9/2 4 ;
1 3| and determine the change of coordinate
matrix   𝑃BS<---B .

Added by Diana B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/20/2023

Step 1

To do this, we need to check that they are linearly independent and span the entire space. Linear independence: We can check this by setting up a linear combination of the matrices in B equal to the zero matrix and solving for the coefficients. If the only Show more…

Show all steps

Thanks for your feedback!

The sets of matrices B = { |1 2 ; 0 0| , |1 0 ; 0 2| , |1 0 ;2 0| , |1 0 ; 0 1| } , Bs = { |1 0 ; 0 0| , |0 1 ; 0 0| , |0 0 ;1 0| , |0 0 ; 0 1| } form bases for the vector space 𝑀2x2(R) of 2 × 2 matrices with real number entries. Give the coordinate vector for [v]B , where v = |9/2 4 ; 1 3| and determine the change of coordinate matrix 𝑃BS<---B .