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] .
- [math]16xx8[/math]
- [math]2xx2xx3[/math]
- [math]4xx3[/math]
- [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]
[math]V=[[12,7,21,31,11],[45,-2,14,27,19],[-3,15,36,71,26],[4,-13,55,34,15]][/math]
- 15
- 14
- -2
- 36
4.
The 5x5 identity matrix of looks like which of the following?
- [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]
- [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]
- [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]
- 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?
- [math][[9,11,12],[4,3,5],[8,9,5]][/math]
- [math][[18,24,27],[3,0,6],[9,18,6]][/math]
- [math][[3,5,6],[-2,-3,-1],[0,3,-1]][/math]
- [math][[9,8,6],[2,0,1],[2,6,3]][/math]
6.
What is the rule for matrix addition and subtraction?
- The number of columns of the first matrix must equal the number of rows of the second matrix.
- The matrices must have the same dimensions.
- The matrices must have the same number of rows, but not columns.
- There is no rule. Matrix addition and subtraction is always possible.
7.
What is the rule for matrix multiplication?
- The number of columns of the first matrix must equal the number of rows of the second matrix.
- The matrices must have the same dimensions.
- The matrices must have the same number of rows, but not columns.
- 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?
- Matrix A is the identity matrix
- [math]A_{1,1} < 0[/math]
- Matrix A has any elements equal to zero
- [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].
- True
- False
10.
Evaluate the determinant of [math][[9, 5], [7, 4]][/math].
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