1000以上 a/bcb/cac/ab = 3/2 247352

`L.H.S. = |,,|`Multiplying first row with `a`, second row with `b` & third row with `c``= 1/(abc)|,,|`Now, taking, `abc` comtháng in `C_3``= (abc)/(abc)|,,|``= |,,|`We know, when we interchange any two rows or columns, sign of dererminant changes.`:.` Interchanging `C_1` & `C_3``=(-1)|<1,a^3,a^2>,<1,b^3,b^2>,<1,c^3,c^2>|`Again interchanging `C_2` và `C_3``=(-1)(-1)|<1,a^2,a^3>,<1,b^2,b^3>,<1,c^2,c^3>|``=|<1,a^2,a^3>,<1,b^2,b^3>,<1,c^2,c^3>| = R.H.S.`
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Let A be a square matrix of order n; then the sum of the product of elements of any row (column) with their cofactors is always equal to `|A|`


Let A be a square matrix of order n; then the sum of the product of elements of any row (column) with the cofactors of the corresponding elements of some other row (column) is 0.

You watching: 1000以上 a/bcb/cac/ab = 3/2 247352


=2` and let B be a matrix obtained from A by interchanging any two rows (columns) of A then `|B|=-|A|`" href="/question-answer/let-aaij-be-a-square-matrix-of-order-n-ge-2-and-let-b-be-a-matrix-obtained-from-a-by-interchanging-a-1340071" data-reactid="868">

Let `A=` be a square matrix of order `n>=2` và let B be a matrix obtained from A by interchanging any two rows (columns) of A then `|B|=-|A|`


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