Linear Algebra and Matrix Theory MATH 302 University of Nairobi (UON) Q&A Quiz
1. What is a matrix?
Answer: A matrix is a rectangular array of numbers or other mathematical objects.
2. What is the determinant of a matrix?
Answer: The determinant of a matrix is a scalar value that represents certain properties of the
matrix, such as invertibility and volume scaling.
3. What is a vector space?
Answer: A vector space is a collection of vectors that satisfy certain properties, such as closure
under addition and scalar multiplication.
4. What is the rank of a matrix?
Answer: The rank of a matrix is the number of linearly independent rows or columns in the
matrix.
5. What is an eigenvector?
Answer: An eigenvector is a non-zero vector that, when multiplied by a matrix, results in a scalar
multiple of itself.
6. What is a diagonal matrix?
Answer: A diagonal matrix is a square matrix where all off-diagonal entries are zero.
7. What is a linear transformation?
Answer: A linear transformation is a function that maps vectors from one vector space to
another, while preserving certain properties such as linearity and homogeneity.
8. What is the dot product of two vectors?
Answer: The dot product of two vectors is a scalar value that represents the cosine of the angle
between the vectors, multiplied by their magnitudes.
9. What is a basis of a vector space?
Answer: A basis of a vector space is a set of vectors that can be used to represent any vector in
the space, through linear combinations.
1. What is a matrix?
Answer: A matrix is a rectangular array of numbers or other mathematical objects.
2. What is the determinant of a matrix?
Answer: The determinant of a matrix is a scalar value that represents certain properties of the
matrix, such as invertibility and volume scaling.
3. What is a vector space?
Answer: A vector space is a collection of vectors that satisfy certain properties, such as closure
under addition and scalar multiplication.
4. What is the rank of a matrix?
Answer: The rank of a matrix is the number of linearly independent rows or columns in the
matrix.
5. What is an eigenvector?
Answer: An eigenvector is a non-zero vector that, when multiplied by a matrix, results in a scalar
multiple of itself.
6. What is a diagonal matrix?
Answer: A diagonal matrix is a square matrix where all off-diagonal entries are zero.
7. What is a linear transformation?
Answer: A linear transformation is a function that maps vectors from one vector space to
another, while preserving certain properties such as linearity and homogeneity.
8. What is the dot product of two vectors?
Answer: The dot product of two vectors is a scalar value that represents the cosine of the angle
between the vectors, multiplied by their magnitudes.
9. What is a basis of a vector space?
Answer: A basis of a vector space is a set of vectors that can be used to represent any vector in
the space, through linear combinations.
