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- Thread starter ajayguhan
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SteamKing

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If you study the properties of determinants, you'll see that for certain row operations, the determinant isn't changed. This property comes in handy when trying to solve a linear system of equations.

http://en.wikipedia.org/wiki/Determinant

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In square matrix multiplication of 3 x3 . consider two matrix A, B such that AB =C ,to obtain the c11 element of C, we take a dot product of row 1 of A and column 1 of B. Row 1 of A is vector whose x, y, z components are a11, a12, a13 respectively. But column 1 of B consist of only x component of three vector of B and I'm taking dot product of a vector and x components to get single element or x component of single vector in C.

Note each matrix A and B consist of 3 different vectors specifying a parallelopiped and x, y, z components are written in column 1,2,3 respectively. Det of A and B is non zero

My question how does the dot product of row 1 and column 1 gives the x component of vector in C is there any proof?

Thanks in advance

Note each matrix A and B consist of 3 different vectors specifying a parallelopiped and x, y, z components are written in column 1,2,3 respectively. Det of A and B is non zero

My question how does the dot product of row 1 and column 1 gives the x component of vector in C is there any proof?

Thanks in advance

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HallsofIvy

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For example, swapping two rows multiplies the determinant by -1. Multiplying a row by "a" multiplies the determinant by "a". It is true that "adding a multiple of one row to another" does not change the determinant.

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