Math39104-Notes - Department of Mathematics, CCNY
... which we put together as the two rows of the 2 × 2 matrix A. All of the following conditions are equivalent. • The pair {(a, b), (c, d)} is linearly dependent. • The determinant det(A) equals zero. • The linear system W A = 0 has a solution W = (w1 w2 ) which is not zero. First, put aside the case w ...
... which we put together as the two rows of the 2 × 2 matrix A. All of the following conditions are equivalent. • The pair {(a, b), (c, d)} is linearly dependent. • The determinant det(A) equals zero. • The linear system W A = 0 has a solution W = (w1 w2 ) which is not zero. First, put aside the case w ...
Verifying Polynomial Identities Here is a problem that has a
... Let’s first consider the case where n = 1, that is, Q is a polynomial of degree d in a single variable. We know something about such polynomials over any field – they can have at most d different roots. (Why? For each root r, the linear polynomial x−r must divide Q. Over a field, this means that th ...
... Let’s first consider the case where n = 1, that is, Q is a polynomial of degree d in a single variable. We know something about such polynomials over any field – they can have at most d different roots. (Why? For each root r, the linear polynomial x−r must divide Q. Over a field, this means that th ...
Unit Overview - Connecticut Core Standards
... spaces and the basis for a vector space. This unit goes as far as solving 2×2 and 3×3 matrices by finding the inverse of a matrix of coefficients and using matrix algebra. The final investigation ties many ideas together from the entire sequence of units in Algebra 2 and geometry by revisiting geome ...
... spaces and the basis for a vector space. This unit goes as far as solving 2×2 and 3×3 matrices by finding the inverse of a matrix of coefficients and using matrix algebra. The final investigation ties many ideas together from the entire sequence of units in Algebra 2 and geometry by revisiting geome ...
