145k views
2 votes
Does the given matrix, A, have an inverse? If it does, what is A-¹? (1 point)

1 Answer

4 votes

Final answer:

Matrix A has an inverse if its determinant is non-zero, which cannot be determined without the specific matrix entries. For vectors A and B of equal magnitude and opposite direction, A - B has the same direction as vector A.

Step-by-step explanation:

To determine if matrix A has an inverse, we need to compute the determinant of matrix A and make sure that it is not zero. A square matrix has an inverse if and only if its determinant is not equal to zero. Unfortunately, you have not provided the specific entries of matrix A, so I cannot compute the determinant for you. Typically, if the matrix is 2x2, the determinant is ad-bc for matrix [[a, b], [c, d]]. For larger matrices, the process involves more complex calculations or using methods such as Gaussian elimination or finding the adjugate matrix. Once the determinant is found to be non-zero, the inverse can be calculated.

In the case of vectors, if vectors A and B are equal in magnitude and opposite in direction, then A - B would have the same direction as vector A. Since B is opposite to A, subtracting B (which is like adding the opposite of B) would effectively result in doubling the vector A in magnitude, pointing in the same direction as A.

User Joe Edgar
by
7.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories