9. Exercise II

Linear Algebra



Weiqi Zhou

Computations

  • find

  • find , where are diagonal matrices with and on the main diagonal respectively, and are anti-diagonal matrices with and on the anti-diagonal respectively

Computations

  • let , find such that

  • let , find such that

Computations

  • suppose that , where , find

  • suppose that , where ,
    find

Proof

let be arbitrary vectors, show that the rank of is

Proof

show that

Proof

show that

Proof

  • let , flip it upwards to obtain

  • show that

Proof

  • let , rotate it counterclockwise to obtain

  • show that

Proof

  • , flip it along the anti-diagonal to get

  • show that