APPM 2360 17 October, 2013 Worksheet #7 1. Consider the space
... Consider R3 as vector space (n = 3). Then S = {(1, 0, 0), (0, 1, 0)} is linearly independent set of R3 . However, it is not a basis for R3 . That is because it has only 2 elements, but dim(R3 ) = 3 (c) TRUE An n × n matrix is row equivalent to In×n ⇐⇒ A is invertible ⇐⇒ rank(A) = n ⇐⇒ rank(A) = dim( ...
... Consider R3 as vector space (n = 3). Then S = {(1, 0, 0), (0, 1, 0)} is linearly independent set of R3 . However, it is not a basis for R3 . That is because it has only 2 elements, but dim(R3 ) = 3 (c) TRUE An n × n matrix is row equivalent to In×n ⇐⇒ A is invertible ⇐⇒ rank(A) = n ⇐⇒ rank(A) = dim( ...
43. Here is the picture: • • • • • • • • • • • • •
... together Z[i]. There are two cosets, so the quotient ring Z[i]/I has two elements, 0 and 1, the images of 0 ∈ Z[i] and 1 ∈ Z[i] under the quotient homomorphism Z[i] Z[i]/I. To see that S = R/I is ∼ = Z/2Z, note that 0 + a = a, 0 × a = 0 and 1 × a = a for every a in any ring, and this determines al ...
... together Z[i]. There are two cosets, so the quotient ring Z[i]/I has two elements, 0 and 1, the images of 0 ∈ Z[i] and 1 ∈ Z[i] under the quotient homomorphism Z[i] Z[i]/I. To see that S = R/I is ∼ = Z/2Z, note that 0 + a = a, 0 × a = 0 and 1 × a = a for every a in any ring, and this determines al ...
Algebra 1 ELG HS.A.3: Perform arithmetic operations on polynomials.
... 6.EE.A Apply and extend previous understandings of arithmetic to algebraic expressions. o 6.EE.A.4 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the di ...
... 6.EE.A Apply and extend previous understandings of arithmetic to algebraic expressions. o 6.EE.A.4 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the di ...
Polynomials - RutledgeMath2
... Reintroducing parts of polynomials and Operating with polynomials ...
... Reintroducing parts of polynomials and Operating with polynomials ...
Lesson 2 – Multiplying a polynomial by a monomial
... - Multiply two polynomials symbolically, and combine like terms in the product (4.5). - Generalize and explain a strategy for multiplication of polynomials (4.6). - Identify and explain errors in a solution for a polynomial multiplication (4.7). - Describe and explain a personal strategy used to det ...
... - Multiply two polynomials symbolically, and combine like terms in the product (4.5). - Generalize and explain a strategy for multiplication of polynomials (4.6). - Identify and explain errors in a solution for a polynomial multiplication (4.7). - Describe and explain a personal strategy used to det ...
