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Using Matrices for Systems of Linear Equations (Grades 11-12)

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Using Matrices for Systems of Linear Equations

1. 
Which matrices below properly represent the system of equations?
[math]3x+8y-23z=14[/math], [math]34x-2y+53z=102[/math], [math]18x+51y+4z=16[/math]
  1. [math][[3,34,18],[8,-2,51],[-23,53,4]]*[[x],[y],[z]]=[[14],[102],[16]][/math]
  2. [math][[3,8,-23],[34,-2,53],[18,51,4]]*[[x],[y],[z]]=[[14],[102],[16]][/math]
  3. [math][ [3,34,18],[8,-2,51],[-23,53,4] ]*[[z],[y],[x]]=[[16],[102],[14]][/math]
  4. [math][ [3,8,-23],[34,-2,53],[18,51,4] ]*[[x],[y],[z]]*[[14],[102],[16]][/math]
2. 
Which matrices below properly represent the system of equations?
[math]19z+2y+34z-8=32[/math], [math]z+2x+4-12y=7[/math], [math]15x+24z-3y=11[/math]
  1. [math][ [0,2,32],[2,-12,7],[15,-3,24] ]*[[x],[y],[z]]=[[32],[7],[11]][/math]
  2. [math][ [0,2,53],[2,-12,1],[15,-3,24] ]*[[x],[y],[z]]=[[40],[3],[11]][/math]
  3. [math][ [0,2,53],[2,-12,1],[15,-3,24] ]*[[z],[y],[x]]=[[40],[3],[11]][/math]
  4. [math][ [0,2,15],[2,-12,-3],[53,1,24] ]*[[x],[y],[z]]=[[11],[7],[32]][/math]
3. 
Which matrices below properly represent the system of equations?
[math]19z+2y+6x=26[/math], [math]x-12z-3y=17[/math], [math]5x+14z+13x-5=13[/math]
  1. [math][ [6,1,18],[2,-3,0],[19,-12,14] ]*[[x],[y],[z]]=[[18],[17],[26]][/math]
  2. [math][ [6,1,18],[2,-3,0],[19,-12,14] ]*[[x],[y],[z]]=[[26],[17],[18]][/math]
  3. [math][ [6,1,18],[2,-3,0],[19,-12,14] ]*[[z],[y],[x]]=[[26],[17],[13]][/math]
  4. [math][ [6,2,19],[1,-3,-12],[18,0,14] ]*[[x],[y],[z]]*[[26],[17],[18]][/math]
4. 
Find the solution of the following matrix equation [math][[1,5],[1,6]][[x],[y]]=[[-4],[-5]][/math].
  1. [math](1,-1)[/math]
  2. [math](1,1)[/math]
  3. [math](0,1)[/math]
  4. [math](-1,-1)[/math]
5. 
Solve. [math][[5,4],[-2,-3]] [[x],[y]] = [[6],[-1]][/math]






6. 
Which augmented matrix represents the system of equations [math]2x+5y=32[/math] and [math]4x-3y=14[/math]?
  1. [math][[-2,-5,, -32],[-4,3,, -14]][/math]
  2. [math][[2,5,,32],[4,-3,,14]][/math]
  3. [math][[32,5,,2],[4,-3,,14]][/math]
  4. [math][[2,32,,5],[14,-3,,4]][/math]
7. 
Which augmented matrix represents the system of equations [math]y-x=18[/math] and [math]x-4=2y[/math]?
  1. [math][[1,-2,,4],[-1,1,,18]][/math]
  2. [math][[1,-1,,18],[1,2,,-4]][/math]
  3. [math][[18,-1,,1],[2,-4,,1]][/math]
  4. [math][[1,18,,-1],[1,2,,-4]][/math]
8. 
Which augmented matrix represents the system of equations [math]2x=8[/math] and [math]6=3y+x[/math]?
  1. [math][[2,8,,0],[6,3,,1]][/math]
  2. [math][[8,2,,0],[6,3,,1]][/math]
  3. [math][[0,2,,8],[6,3,,1]][/math]
  4. [math][[2,0,,8],[1,3,,6]][/math]
9. 
Find the row-reduced echelon form of the following augmented matrix to find the solution to the corresponding system of equations.
[math] [[2,1,,13],[1,-5,,-10]][/math]
  1. [math](10,3)[/math]
  2. [math](13,-33)[/math]
  3. [math](5,3)[/math]
  4. No solution
10. 
Use Gaussian Elimination to find the Row-Reduced Echelon form of the following matrix, thus solving the corresponding system of equations.
[math][[3,-2,,-20],[-5,1,,17]][/math]






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