Final answer:
The student's query relates to linear algebra concepts like null space and matrix rank, but the provided true/false statements are about the Pythagorean theorem and geometric areas. The first statement is true for orthogonal vectors, and the second requires additional information, while the third cannot be answered without context.
Step-by-step explanation:
The student's question involves finding a basis for the null space of a matrix A, computing the rank of the matrix, and verifying a theorem related to these concepts in linear algebra. However, the provided statements are not directly related to the question asked but I can address the true/false statements provided.
Statement 1
True or False-We can use Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other. The answer is a. True. When two vectors are at right angles, or orthogonal, the Pythagorean theorem can indeed be used to find the magnitude of the resultant vector.
Statement 2
Compare the areas A₁, A₂, and A3 in terms of size. Without specific information about these areas, the statement cannot be definitively answered. However, if it is given that the areas are of the same size, then b. A₁ = A₂ = A3 would be true.
Statement 3
True or False- Statements need context to be evaluated as true or false. Therefore, these types of questions require specific information or claims to be properly addressed.