QUESTION 9 Consider a 2×6 matrix A . What is the minimum value for the nullity of A? a. 0 b. 2 C. 4 d. 6 give correct answer with explanation don't use chatgpt I'll report the answer
In linear algebra, the nullity of a matrix A is the dimension of the null space, which is also known as the kernel. It represents the number of linearly independent vectors in the solution space of the homogeneous equation Ax = 0, where x is a vector of appropriate dimension.
In your case, you have a 2x6 matrix A. The minimum value for the nullity of A can be determined by examining the rank of the matrix. The nullity of the matrix will then be the difference between the number of columns and the rank (since it's a 2x6 matrix). So, the nullity is given by:
Nullity(A) = Number of columns - Rank(A)
For the given matrix A, the minimum value for the nullity occurs when the matrix has full rank, which means all rows or columns are linearly independent. In this case, the rank of A will be 2 (the number of rows). So, the nullity is:
Nullity(A) = 6 (number of columns) - 2 (rank of A) = 4
Therefore, the minimum value for the nullity of A is 4, which corresponds to option (c).
Answers & Comments
Option (c) 4.
In linear algebra, the nullity of a matrix A is the dimension of the null space, which is also known as the kernel. It represents the number of linearly independent vectors in the solution space of the homogeneous equation Ax = 0, where x is a vector of appropriate dimension.
In your case, you have a 2x6 matrix A. The minimum value for the nullity of A can be determined by examining the rank of the matrix. The nullity of the matrix will then be the difference between the number of columns and the rank (since it's a 2x6 matrix). So, the nullity is given by:
Nullity(A) = Number of columns - Rank(A)
For the given matrix A, the minimum value for the nullity occurs when the matrix has full rank, which means all rows or columns are linearly independent. In this case, the rank of A will be 2 (the number of rows). So, the nullity is:
Nullity(A) = 6 (number of columns) - 2 (rank of A) = 4
Therefore, the minimum value for the nullity of A is 4, which corresponds to option (c).
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