Question #269890

Question 4 Use row operation to show that

det T = 0


x

2 2x + 1 4x + 4 6x + 9

y

2 2y + 1 4y + 4 6y + 9

z

2 2z + 1 4z + 4 6z + 9

w

2 2w + 1 4w + 4 6w + 9


1
Expert's answer
2021-11-24T10:08:43-0500

T=x22x+14x+46x+9y22y+14y+46y+9z22z+14z+46z+9w22w+14w+46w+9|T|=\begin{vmatrix} x^2 & 2x+1 & 4x+4 &6x + 9\\ y^2 & 2y+1 & 4y+4 &6y + 9\\ z^2 & 2z+1 & 4z+4 &6z + 9\\ w^2 & 2w+1 & 4w + 4&6w + 9 \end{vmatrix}


if we add 2nd and 3rd columns, and subtract it from 4th column, we get:


T=x22x+14x+44y22y+14y+44z22z+14z+44w22w+14w+44|T|=\begin{vmatrix} x^2 & 2x+1 & 4x+4 & 4\\ y^2 & 2y+1 & 4y+4 &4\\ z^2 & 2z+1 & 4z+4 &4\\ w^2 & 2w+1 & 4w + 4&4 \end{vmatrix}


if we multiply 2nd column by 2, and subtract it from 3rd column, we get:


T=x22x+124y22y+124z22z+124w22w+124|T|=\begin{vmatrix} x^2 & 2x+1 & 2 & 4\\ y^2 & 2y+1 & 2 &4\\ z^2 & 2z+1 & 2 &4\\ w^2 & 2w+1 & 2&4 \end{vmatrix}


then, multiplying 3rd column by 2, we get:


2T=x22x+144y22y+144z22z+144w22w+144=02|T|=\begin{vmatrix} x^2 & 2x+1 & 4 & 4\\ y^2 & 2y+1 & 4 &4\\ z^2 & 2z+1 & 4 &4\\ w^2 & 2w+1 & 4&4 \end{vmatrix}=0


since two columns of a determinant are identical.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS