Where is wrong 2?

Algebra Level 3

Statement One: You are trying to evaluate 9 8 7 5 4 6 1 2 3 \displaystyle \begin{vmatrix} 9 & 8 & 7 \\ 5 & 4 & 6 \\ 1 & 2 & 3 \end{vmatrix} .

Statement Two: Then, you think that ( 9 8 7 5 4 6 1 2 3 ) = ( 5 3 4 4 5 5 3 4 3 ) + ( 4 5 3 1 1 1 2 2 0 ) \displaystyle \begin{pmatrix} 9 & 8 & 7 \\ 5 & 4 & 6 \\ 1 & 2 & 3 \end{pmatrix} = \begin{pmatrix} 5 & 3 & 4 \\ 4 & 5 & 5 \\ 3 & 4 & 3 \end{pmatrix} + \begin{pmatrix} 4 & 5 & 3 \\ 1 & -1 & 1 \\ -2 & -2 & 0 \end{pmatrix}

Statement Three: 9 8 7 5 4 6 1 2 3 = 5 3 4 4 5 5 3 4 3 + 4 5 3 1 1 1 2 2 0 \therefore \displaystyle \begin{vmatrix} 9 & 8 & 7 \\ 5 & 4 & 6 \\ 1 & 2 & 3 \end{vmatrix} = \begin{vmatrix} 5 & 3 & 4 \\ 4 & 5 & 5 \\ 3 & 4 & 3 \end{vmatrix} + \begin{vmatrix} 4 & 5 & 3 \\ 1 & -1 & 1 \\ -2 & -2 & 0 \end{vmatrix}

Statement Four: ( 30 ) = ( 12 ) + ( 14 ) \displaystyle \implies (-30) = (-12) + (-14)

Statement Five: 30 = 26 ? \displaystyle \therefore -30 = -26 ?

Which of these statements is the start of the mistake in the said argument?


Notations: A | A | is the determinant of the matrix A while ( A ) \big( A \big ) is the matrix A itself.


The answer is 3.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Christian Daang
Mar 20, 2017

It is not always true that the sum of the determinants of two matrices is the same as the determinant of the summands of the two matrices.

therefore, statement three is wrong.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...