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Understanding Matrices (Grades 11-12)

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Understanding Matrices

1. 
State the dimensions of matrix [math]F[/math] if [math]F=[[0,1,0],[2,-4,2],[4,-8,4],[8,-16,8]][/math] .
  1. [math]16xx8[/math]
  2. [math]2xx2xx3[/math]
  3. [math]4xx3[/math]
  4. [math]3xx4[/math]
2. 
Write a matrix with 2 rows and 5 columns.





3. 
Element [math]"V"_{3,2}[/math] in Matrix V shown below is                .

[math]V=[[12,7,21,31,11],[45,-2,14,27,19],[-3,15,36,71,26],[4,-13,55,34,15]][/math]
  1. 15
  2. 14
  3. -2
  4. 36
4. 
The 5x5 identity matrix of looks like which of the following?
  1. [math][[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]][/math]
  2. [math][[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]][/math]
  3. [math][[0,0,1,0,0],[0,0,1,0,0],[1,1,1,1,1],[0,0,1,0,0],[0,0,1,0,0]][/math]
  4. A and B
5. 
If the matrix [math][[6,8,9],[1,0,2],[3,6,2]][/math] is multiplied by the scalar 3, what is the result?
  1. [math][[9,11,12],[4,3,5],[8,9,5]][/math]
  2. [math][[18,24,27],[3,0,6],[9,18,6]][/math]
  3. [math][[3,5,6],[-2,-3,-1],[0,3,-1]][/math]
  4. [math][[9,8,6],[2,0,1],[2,6,3]][/math]
6. 
What is the rule for matrix addition and subtraction?
  1. The number of columns of the first matrix must equal the number of rows of the second matrix.
  2. The matrices must have the same dimensions.
  3. The matrices must have the same number of rows, but not columns.
  4. There is no rule. Matrix addition and subtraction is always possible.
7. 
What is the rule for matrix multiplication?
  1. The number of columns of the first matrix must equal the number of rows of the second matrix.
  2. The matrices must have the same dimensions.
  3. The matrices must have the same number of rows, but not columns.
  4. There is no rule. Matrix multiplication is always possible.
8. 
A square matrix A is NOT invertible (does not have an inverse) if which of the following is true?
  1. Matrix A is the identity matrix
  2. [math]A_{1,1} < 0[/math]
  3. Matrix A has any elements equal to zero
  4. [math]det(A) = 0[/math]
9. 
Matrix multiplication is commutative, e.g. for the [math]n xx n[/math] matrices [math]A and B, \ \ AB = BA[/math].
  1. True
  2. False
10. 
Evaluate the determinant of [math][[9, 5], [7, 4]][/math].





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