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Table 1: Some key terms from exam 2 material Determinant Column Space Rank Crame

ID: 3116947 • Letter: T

Question

Table 1: Some key terms from exam 2 material Determinant Column Space Rank Cramers Rule Non-Singular Invertible verse Cofactor Cofactor Expansion Adjoint Basis Subspace Null Space Nullity Dimension Coordinate Vector Digenvalue Ei Eigenspace Definition Matching: (1pt each) Choose the most appropriate key term in Table 1 matrix. 1. A matrix that is not invertible is known as a 2. Given A e Rnxm the set of all solutions to the homogeneous equation Ax = 0 is known as the of A. 3. Given A ERmxn if M ERnxnst. AM = MA = 1 then M is defined to be the of A. 4. Given a subspace W, if S is linearly independent set of vectors whose span is W then S is a of W. 5. If A e Rnxm, 0 and c E R st. Ax = cx then c is defined to be a of A. 6. Given a subspace W, the number of vectors in a basis of W is defined to be the of W. 7. Given A E Rn*m, the number of vectors in a basis of Col(A) is known as the of A.

Explanation / Answer

1.A matrix that is not invertible is known as a singular matrix.

2.The set of all solutions to the equation Ax = 0 is known as the null space of A.

3.If AM = MA=I, then M is defined to be the inverse of A.

4. If S is a linearly independent set of vectors whose span is the vector space W, then S is known as the basis for W.

5. If Ax = cx (x0), then c is defined to be an eigenvalue of A.

6. The number of vectors in a basis for a vector space W is defined to be the dimension of W.

7. The number of vectors in a basis of col(A) is known as the rank of A.