Multiplication by a Scalar (Grades 11-12)

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Multiplication by a Scalar

1. 
For [math]M = [[3,9],[5,1]][/math], what is the result of multiplying [math]M[/math] by 3?
  1. [math][[9,9],[5,1]][/math]
  2. [math][[9,27],[15,3]][/math]
  3. [math][[9,27],[5,1]][/math]
  4. [math][[9,9],[15,1]][/math]
2. 
For [math]A = [[1,7],[0,3]][/math], which of the following is equal to [math]4A ?[/math]
  1. [math][[4,28],[4,12]][/math]
  2. [math][[4,7],[0,3]][/math]
  3. [math][[4,28],[0,12]][/math]
  4. [math][[4,7],[4,3]][/math]
3. 
Find the resulting matrix if the matrix [math][[4,-2],[8,6]][/math] is multiplied by [math]3/2[/math].
  1. [math] [[6,-3],[12,9]] [/math]
  2. [math] [[12,-6],[24,18]][/math]
  3. [math] [[6,-2],[12,6]] [/math]
  4. [math] [[6,-3],[8,6]] [/math]
4. 
For [math]D = [[3, -4, 0],[2,1/2,-5]][/math], find [math]-6D[/math].
  1. [math] [[18,-4,0],[-12,1/2,-5]][/math]
  2. [math] [[18,-24,-6],[2,1/2,-5]][/math]
  3. [math] [[-18,24,0],[-12,-3,30]][/math]
  4. [math] [[18,-24,-6],[12,3,-30]][/math]
5. 
For [math]V = [[4],[-2],[8],[1/3]][/math], find [math]1/2 V[/math].
  1. [math] [[2],[-2],[8],[1/3]] [/math]
  2. [math][[2],[-1],[4],[1/6]][/math]
  3. [math] [[2],[-1],[4],[1/3]] [/math]
  4. [math] [[4],[-2],[8],[1/6]] [/math]
6. 
For [math]M = [[3,0,-9],[6,-6,12],[1,15,-3]][/math] find [math]4/3 M[/math].
  1. [math] [[4,0,-12],[6,-6,12],[1,15,-3]][/math]
  2. [math] [[4,0,-9],[8,-6,12],[4/3,15,-3]][/math]
  3. [math] [[4,4/3,-12],[8,-8,16],[4/3,20,-4]] [/math]
  4. [math] [[4,0,-12],[8,-8,16],[4/3,20,-4]] [/math]
7. 
If [math]G = [[4,5],[-2,6]][/math] and [math]a G = [[8,10],[-4,12]][/math], what is the value of [math]a ?[/math]
  1. -1/2
  2. 1/2
  3. -2
  4. 2
8. 
For [math]M = [[-12,-36,6],[-3,0,-15],[-9,24,9]][/math] and [math]a M = [[4,12,-2],[1,0,5],[3,-8,-3]][/math] , what is the value of [math]a ?[/math]
  1. [math]-3[/math]
  2. [math]-1/3[/math]
  3. [math]3[/math]
  4. [math]1/3[/math]
9. 
Matrix B is given with two of its elements unknown, [math]B = [[B_(1,1), 0],[-4, B_(2,2)]][/math]. Another matrix is given, which is matrix B which has been multiplied by a scalar, [math][[3,0],[-1,2]][/math]. What are the two unknown elements in matrix B, listed as [math]B_(1,1), B_(2,2) ?[/math]
  1. [math]12, 8[/math]
  2. [math]3/4, 1/2 [/math]
  3. [math]-12, -8[/math]
  4. [math]-3/4, -1/2 [/math]
10. 
Jason is currently in his last year of high school and is considering which university he will go to next year. He has made a matrix of his top three choices, each university in a different row, and the four most important facts for him: tuition costs per year, in dollars (first column), number of students (second column), number of faculty in his desired major (third column), and the distance from his current home, in miles (fourth column). Let this be matrix U, as follows.

[math]U = [["20,000", "30,000", 25, 30 ],["25,000", "20,000", 12, 100],["21,000", "15,000", 10, 180]] [/math]

Jason then finds out that his aunt will cover half of his tuition costs, to whatever university he wants to go to. How can Jason update matrix U with this new information using multiplication by a scalar?
  1. [math]1/2 A[/math]
  2. [math]2 A[/math]
  3. [math]A 1/2[/math]
  4. This cannot be represented with multiplication by a scalar.

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