
Matrix Transformation and Kernel

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Olivia Brooks
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the kernel of a matrix transformation?
The set of all output vectors that map to the zero vector
The set of all input vectors that map to the identity matrix
The set of all input vectors that map to the zero vector
The set of all output vectors
Tags
CCSS.HSN.VM.C.10
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding a basis for the kernel of a matrix transformation?
Finding the determinant of the matrix
Solving the equation matrix A times vector x equals the zero vector
Calculating the inverse of the matrix
Finding the eigenvalues of the matrix
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the augmented matrix represent in the context of finding the kernel?
The system of equations to be solved
The inverse of the matrix
The solution to the system of equations
The original matrix
Tags
CCSS.8.EE.C.8B
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is indicated by a row of zeros in the reduced row echelon form of an augmented matrix?
A free variable
A unique solution
No solution
An inconsistent system
Tags
CCSS.8.EE.C.8A
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which variable is identified as a free variable in the reduced row echelon form?
None of the above
x3
x2
x1
Tags
CCSS.8.EE.C.8B
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the solution parameterized when x3 is a free variable?
x1 = -t, x2 = t, x3 = -t
x1 = -t, x2 = -t, x3 = t
x1 = t, x2 = -t, x3 = -t
x1 = t, x2 = t, x3 = t
Tags
CCSS.8.EE.C.8B
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the basis vector for the kernel of the transformation?
(1, 1, 1)
(-1, -1, 1)
(1, -1, 1)
(0, 0, 0)
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