# 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

Linear Algebra Conditions

asked
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2017-02-15 05:30:02 -0500
**

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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

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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.

Asked: **
2017-02-15 05:30:02 -0500
**

Seen: **238 times**

Last updated: **Feb 23 '17**

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This looks like homework. Could you please tell us how it is related to Sage, and what were your attempts in solving this ?