Question

Given the vector ;
a=[0,1,2]
B=(aᵀ)a
C=a(aᵀ)
what is the rank of B and C?

Answer 1

The rank of matrix B and C in the given question is 1.

Step-by-step explanation:

The rank of a matrix can be found by determining the number of linearly independent rows or columns in the matrix. In the given question, we have the vectors a=[0,1,2], b=(aᵀ)a, and c=a(aᵀ).

To find the rank of matrix B, we need to determine the number of linearly independent rows or columns in matrix B. Since B is obtained by multiplying a transposed by a, it is a square matrix. The rank of matrix B is equal to the number of linearly independent columns or rows in B. In this case, B has rank 1.

To find the rank of matrix C, we need to determine the number of linearly independent rows or columns in matrix C. Since C is obtained by multiplying a by a transposed, it is also a square matrix. The rank of matrix C is equal to the number of linearly independent columns or rows in C. In this case, C has rank 1.