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Matrix-vector multiplication is a linear operation. What does this mean?
It always produces the zero vector.
It preserves vector lengths.
It follows the distributive law.
It only involves integer values.
Fill in the blank:
The matrix that performs a rotation transformation is called a __________.
Scaling matrix
Translation matrix
Rotation matrix
Reflection matrix
Is this statement true or false?
The result of matrix-vector multiplication is always a vector.
True
False
The transformation of a vector using matrix multiplication can include:
Scaling
Rotation
Translation
All of the above
If a matrix transformation flips a vector over a specific axis, it is referred to as ________.
Reflection
The identity matrix, when multiplied with a vector, results in vector itself.
Which property of matrices allows us to perform matrix-vector multiplication associatively, i.e., (Av = A(Bv)?
Commutativity
Distributivity
Associativity
Transitivity
In matrix multiplication, the order matters. If A is a matrix and B is a vector, then the multiplication is valid for BA as well.
If a matrix A is a square matrix, then the transformation it represents can:
Change the dimension of the vector
Only scale the vector
Only rotate the vector
Preserve the dimension of the vector
If matrix AAA is a 3x2 matrix and vector vvv is a 2-dimensional vector, what is the dimension of the result AvAvAv?
3-dimensional vector
2-dimensional vector
1-dimensional vector
4-dimensional vector
It is done.