- #1
forty
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1)
Show that if matrix products AB and BA are both defines, then AB and BA are square matrices:
Let A = a m*n matrix
IF AB is defined then B must have n rows (n*?) matrix
IF BA is defined then B must have m columns making it a n*m matrix
so BA = (n*m) * (m*n) = (n*n) matrix
AB = (m*n) * (n*m) = (m*m) matrix
2)
Show that if A is an m*n matrix and A(BA) is defined, then B is an n*m matrix.
IF BA is defined and A is m*n matrix then B must be a ?*m matrix
BA produces a ?*n matrix
IF A(BA) is defined BA must be a n*n matrix
AS BA is an n*n matrix B must be a n*m matrix
Do these work as a proofs, if they even follow any logic in the first place (I'm horrid when it comes to matrices)
Any input would be greatly appreciated :)
Show that if matrix products AB and BA are both defines, then AB and BA are square matrices:
Let A = a m*n matrix
IF AB is defined then B must have n rows (n*?) matrix
IF BA is defined then B must have m columns making it a n*m matrix
so BA = (n*m) * (m*n) = (n*n) matrix
AB = (m*n) * (n*m) = (m*m) matrix
2)
Show that if A is an m*n matrix and A(BA) is defined, then B is an n*m matrix.
IF BA is defined and A is m*n matrix then B must be a ?*m matrix
BA produces a ?*n matrix
IF A(BA) is defined BA must be a n*n matrix
AS BA is an n*n matrix B must be a n*m matrix
Do these work as a proofs, if they even follow any logic in the first place (I'm horrid when it comes to matrices)
Any input would be greatly appreciated :)