Determinant Q54: Cofactor Expansion Solution

  • Thread starter azzarooni88
  • Start date
  • Tags Tags
    Determinant
5 replies · 2K views · last reply
azzarooni88
Messages
10
Reaction score
3

Homework Statement



Textbook page with exercises 51-54, Solve for x, showing four 3x3 determinants set equal to zero: 51 has x, 12, 13 / 0, x-1, 23 / 0, 0, x-2; 52 has x, 1, 1 / 1, 1, x / x, 1, x; 53 has 1, 0, x / x^2, 1, 0 / x, 0, 1; 54 has a, b, x-a / x, x+b, x / 0, 1, 1.


Q54.

Homework Equations



Cofactor expansion (along 1st column)

The Attempt at a Solution



Handwritten derivation on lined paper: a 3x3 determinant with rows (a, b, x-a), (x, x+b, x), (0, 1, 1) set equal to zero, expanded by cofactors to a(x+b-x) - x(b-(x-a)), simplifying to x^2 - x(b+a) + ab, with 'Find x?' written beside it. Above is a column vector equation [x, y, z] = [4, 2, -1].
 
Attachments
  • Handwritten derivation on lined paper: a 3x3 determinant with rows (a, b, x-a), (x, x+b, x), (0, 1, 1) set equal to zero, expanded by cofactors to a(x+b-x) - x(b-(x-a)), simplifying to x^2 - x(b+a) + ab, with 'Find x?' written beside it. Above is a column vector equation [x, y, z] = [4, 2, -1].
    20180515_125718_1920x1080.jpg
    33.4 KB · Views: 847
  • Textbook page showing exercises 51 to 54, 'Solve for x', with four 3 by 3 determinants set equal to zero; exercise 54 has rows (a, b, x - a), (x, x + b, x), (0, 1, 1).
    20180515_123029_1920x1080.jpg
    22.6 KB · Views: 478
  • Textbook page with exercises 51-54, Solve for x, showing four 3x3 determinants set equal to zero: 51 has x, 12, 13 / 0, x-1, 23 / 0, 0, x-2; 52 has x, 1, 1 / 1, 1, x / x, 1, x; 53 has 1, 0, x / x^2, 1, 0 / x, 0, 1; 54 has a, b, x-a / x, x+b, x / 0, 1, 1.
    ?temp_hash=02f18fab410d1aa0cdd3721da958b5f6.jpg
    22.6 KB · Views: 880

Discussion

Mark44 said:
What happened to your equation. You're starting with the determinant equalling 0. You lost one side of your equation.
solving the determinant equal to 0
 
azzarooni88 said:
solving the determinant equal to 0
If you're solving an equation, you have to actually have an equation.
In your first line, you start off with "= ..." followed by a bunch of expressions. You seem to have lost one side of your equation.
 
Mark44 said:
If you're solving an equation, you have to actually have an equation.
In your first line, you start off with "= ..." followed by a bunch of expressions. You seem to have lost one side of your equation.
I think my working is logical. I start off with 0=... and just don't continue writing 0 on the LHS as I solve for the RHS. Ultimately I get 0=x2 - x(b+a) +ab
 
azzarooni88 said:
I think my working is logical. I start off with 0=... and just don't continue writing 0 on the LHS as I solve for the RHS. Ultimately I get 0=x2 - x(b+a) +ab

Okay, can you solve that equation for ##x##?
 

Similar threads

311.3.1.1 - Determinants And Cofactor Expansion
  • karush
  • · Replies 3 ·
  • Linear and Abstract Algebra
Replies
3
Finding cofactor expansion along the second column
  • karush
  • · Replies 2 ·
  • Linear and Abstract Algebra
Replies
2
Cofactor Expansion: Find Determinant of 4x3 Matrix
  • fk378
  • · Replies 3 ·
  • Calculus and Beyond Homework Help
Replies
3
Graduate Legendre Expansion solution to sphere of potential V with charge q outside
  • phys_student1
  • · Replies 2 ·
  • Electromagnetism
Replies
2
Undergrad Why am I getting determinant 0 with cofactor expansion on a 4x4 matrix?
  • phantomAI
  • · Replies 3 ·
  • Linear and Abstract Algebra
Replies
3
How to find C - the cofactor matrix of A?
  • Cinitiator
  • · Replies 5 ·
  • Calculus and Beyond Homework Help
Replies
5
Cofactor matrix and determinant question
  • fluidistic
  • · Replies 2 ·
  • Calculus and Beyond Homework Help
Replies
2
How Does the Rank of a Matrix Influence Its Cofactor Matrix Becoming Zero?
  • harvesl
  • · Replies 1 ·
  • Calculus and Beyond Homework Help
Replies
1
Is zinc ion a cofactor or coenzyme in alcohol dehydrogenase?
  • gabby21090
  • · Replies 1 ·
  • Biology and Chemistry Homework Help
Replies
1
How Can I Calculate Determinant, Cofactors, Adjugate, and Inverse of a Matrix?
  • LaraCroft
  • · Replies 2 ·
  • Introductory Physics Homework Help
Replies
2