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Let A = [[a, b],[c, d]]be a 2x2 matrix. Let vector v = <a,b> and vector w =...
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You need to use the equation that relates two parallel vectors, such that:
`bar v || bar w <=> a/c = b/d => ad = bc => ad - bc = 0`
You need to prove that matrix A is invertible if the vectors are not parallel.
You should remember that a matrix is invertible if `det A != 0` , hence, evaluating the determinant of matrix A, yields:
`det A = [(a,c),(b,d)] ` `=> det A = ad - bc`
You need to notice that `det A != 0` if `ad - bc != 0` , hence, since `ad - bc != 0` , then the vector `bar v = <a,b>` is not parallel to `bar w = <c,d>` .
Posted by sciencesolve on April 8, 2013 at 3:32 PM (Answer #1)
We wish to prove that A is invertible ,if columns vector v and vector w are not parallel i.e cross product of vector v and vector w does not vanish.
`v xxw =|[a,b],[c,d]|`
If `ad-bc!=0` ,then vector v and w can not be parallel.
Posted by pramodpandey on April 11, 2013 at 5:06 AM (Answer #1)
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