Final answer:
The answer is True; vectors in the null space of a matrix are perpendicular to those in the row space, as their dot product is zero, which is the definition of perpendicularity in vector mathematics.
Step-by-step explanation:
The correct answer is option a. True. Every vector in the null space of a matrix A is perpendicular to every vector in the row space of A. This is because the null space consists of all vectors x such that Ax = 0, meaning these vectors yield the zero vector when multiplied by A. The row space is formed by the rows of A, which represent the coefficients of A in a linear combination. When vectors from the null space and the row space are combined in a dot product, the result is zero, satisfying the definition of perpendicularity as their dot product is zero.
Other true statements related to vector mathematics are:
- A vector can form the shape of a right angle triangle with its x and y components.
- The Pythagorean theorem can be used to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other.
- The vector product of two vectors is a vector perpendicular to the plane that contains the original vectors.