M is the space of 3 by 3 matrices. Multiply every matrix X in M by...

  

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M is the space of 3 by 3 matrices. Multiply every matrix X in M by 0-1 1 0 -1 1 H-BL A Notice: A 0 (a) Which matrices X lead to AX - zero matrix? (b) Which matrices have the form AX for some matrix X? (a) finds the "nullspace" of that operation AX and (b) finds the "column space". What are the dimensions of those two subspaces of M? Why do the dimensions add to (n-r) +r=9? M is the space of 3 by 3 matrices. Multiply every matrix X in M by 0-1 1 0 -1 1 H-BL A Notice: A 0 (a) Which matrices X lead to AX - zero matrix? (b) Which matrices have the form AX for some matrix X? (a) finds the "nullspace" of that operation AX and (b) finds the "column space". What are the dimensions of those two subspaces of M? Why do the dimensions add to (n-r) +r=9?

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To find the matrices X that lead to AX zero matrix we need to solve the equation AX 0 This means mul... View the full answer