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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
Is this statement true or false?
The identity matrix, when multiplied with a vector, results in vector itself.
True
False
Fill in the blank:
The matrix that performs a rotation transformation is called a __________.
Scaling matrix
Translation matrix
Rotation matrix
Reflection matrix
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
The transformation of a vector using matrix multiplication can include:
Scaling
Rotation
Translation
All of the above
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.
Which property of matrices allows us to perform matrix-vector multiplication associatively, i.e., (Av = A(Bv)?
Commutativity
Distributivity
Associativity
Transitivity
The result of matrix-vector multiplication is always a vector.
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 transformation flips a vector over a specific axis, it is referred to as ________.
Reflection
It is done.