No. Say your matrix is called A, then a number e is an eigenvalue of A exactly when A-eI is singular, where I is the identity matrix of the same dimensions as A. A-eI is singular exactly when (A-eI)T is singular, but (A-eI)T=AT-(eI)T =AT-eI. Therefore we can conclude that e is an eigenvalue of A exactly when it is an eigenvalue of AT.
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The determinant function is only defined for an nxn (i.e. square) matrix. So by definition of the determinant it would not exist for a 2x3 matrix.
It may or may not exist. If the matrix of coefficients is singular then there is no solution.
no, the correct matrix to use is PQRS P1010 Q0101 R1100 S0010
There are virtually an infinite amount of different skin colours that exist since the possibilities of shades are infinite.
As so many different language translations exist, and as, within those languages, so many different versions exist, and as, within those versions, so many printings exist.... this number is unknown and unknowable.