Linear Algebra Conditions
imgur.com/a/xIydC The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D
to echo tmoneil's comment, this post is more suited to mathstackexchange
2 Answers
The system of equations
x+by=-1
2ax+2y=5
is equivalent to the matrix-vector equation Ax=b, where A = matrix(2,1,(1,b,2a,2)), x = (x,y) and b = (-1,5). This equation has a unique solution exactly when det(A) is non-zero.
Now, det(A) = 2-2ab, which is nonzero precisely when ab != 1.
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http://domyhomeworkfor.me/ told me this can easily be done with determinants. If a square matrix's determinant does not equal zero, then that square matrix will have an inverse hence having a unique solution. Since this is a 2x2 matrix, just compute the determinant with the condition that it cannot equal zero: (1)(2)-(2ab) =/= 0 2 =/= 2ab 1=/= ab
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Asked: 8 years ago
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Last updated: Feb 23 '17
This looks like homework. Could you please tell us how it is related to Sage, and what were your attempts in solving this ?