Calculating the value of determinant by using row-column tri

navneet9431 · Aug 3, 2018

Homework Statement

I am trying to find the value of a determinant,

Handwritten determinant of a 3 by 3 matrix with first column all 1s, second row entries x-4 and 2x, and rows 1 2x 2x, 1 x-4 2x, 1 2x x-4, followed by the start of a row operation note reading C2 and C3 with a zero-padded row below.

Homework Equations

See the notes given in my Textbook,

Photo of a handwritten-style printed textbook page on determinants, showing the row-column operation property with a 3x3 determinant example and a note on the effect of row operations.

The Attempt at a Solution

I applied this method to find the value of a determiannt,

See it here,

Handwritten working on lined paper: a 3x3 determinant with rows (1, 2x, 2x), (1, x-4, 2x), (1, 2x, x-4), with the note 'Apply C2 to C2 minus C3 and C3 to C3 minus C2', giving a determinant with rows (1, 0, 0), (1, -(x+4), (x+4)), (1, (x+4), -(x+4)) set equal to 0, marked WRONG with 'Why?'

Why is my result wrong?

I will be thankful for any help!

andrewkirk · Aug 3, 2018

The column operations must be done sequentially, and at each step must use the columns from the new matrix created in the previous step.

So in the second step when you subtract C2 from C3 it has to be the new C2, not the original one.

navneet9431 · Aug 3, 2018

Thanks !

andrewkirk said:

The column operations must be done sequentially, and at each step must use the columns from the new matrix created in the previous step.

So in the second step when you subtract C2 from C3 it has to be the new C2, not the original one.

Calculating the value of determinant by using row-column tri

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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