Could somebody help me solve this problem? Let #A = ((−1, −1),(3, 3))# . Find all 2 × 2 matrices, #B# such that #AB = 0#.

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Answer 1 · 2018-02-26T10:35:50

#B = ((a,b),(-a,-b))#

#"Name the elements of B as follows : "#

#B = ((a , b), (c , d))#

#"Multiply : "#

#((-1, -1), (3, 3)) * ((a,b),(c,d)) = ((-a-c, -b-d),(3a+3c, 3b+3d))#

#"So we have the following system of linear equations :"#

#a+c = 0#
#b+d = 0#
#a+c = 0#
#b+d = 0#

#=> a = -c , " "b = -d#

#"So"#

#B = ((a , b),(-a, -b))#

#"So, all B of that shape satisfy. The first row can have"#
#"arbitrary values, and the second row must be the negative"#
#"of the first row."#