
Understanding Least Squares Solutions

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
+1
Standards-aligned

Aiden Montgomery
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary condition for using least squares solutions?
Matrix A must be invertible.
Matrix A must be square.
Matrix A must have orthogonal columns.
Vector b must be zero.
Tags
CCSS.8.EE.C.8C
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the least squares solution vector x hat denoted?
As a polynomial
As a vector
As a scalar
As a matrix
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the dot products in the least squares solution formula?
They verify the orthogonality of vector b.
They determine the size of matrix A.
They simplify the matrix multiplication.
They are used to calculate the components of vector x hat.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a zero result from the dot product of two vectors indicate?
The vectors are parallel.
The vectors are orthogonal.
The vectors are identical.
The vectors are zero vectors.
Tags
CCSS.8.EE.C.8B
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the contradiction in row four of the augmented matrix indicate?
There is a unique solution.
There are infinite solutions.
The solution is zero.
There is no solution.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of vector b dotted with vector u sub one divided by vector u sub one dotted with itself?
Zero
Negative three halves
Negative three
Two
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the least squares solution for the given matrix and vector?
Vector negative three halves, negative three halves, two
Vector one
Vector two, two, two
Vector zero
Tags
CCSS.HSA.REI.C.9
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