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A detailed tutorial on how to solve equations using the additive inverse. Step by step tutorial including several examples of how to solve equations with the additive inverse for reference.

The additive inverse is the inverse of the additive identity – which should be very easy to guess. However, the problem is not guessing the definition of the additive inverse – the problem is knowing what the inverse of the additive identity is. The additive identity states that any number plus zero equals itself. The additive inverse states that any positive number minus its true value or any negative number plus its true value is equal to zero – in other words, that two inverses together equal zero. You solve equations by using the additive inverse.

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A detailed tutorial on the additive identity. Step by step tutorial including several examples of the additive identity for reference.

The additive identity is very similar to the zero properties of multiplication and addition. However, the additive property is only used with addition – which should be easy to tell from the name of this identity. The additive identity states that any number plus zero, or with zero added to it, is equal to itself. The additive property is one of the properties that all teachers expect you to already know, so it is important to learn it.

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A detailed tutorial on orthogonal vectors. Step by step tutorial including several examples of orthogonal vectors for reference.

Orthogonal vectors are vectors that are perpendicular. You can determine if vectors are perpendicular by finding the dot product. If the dot product is equal to zero, then the vectors are perpendicular. In certain dimensions, it is possible for three vectors to be perpendicular to each other. In this case, all three of those vectors are considered to be orthogonal. However, in general, orthogonal vectors is a term used to describe a pair of vectors.

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A detailed tutorial on zero pairs. Step by step tutorial including several examples of how to solve equations using zero pairs for reference.

Zero pairs are a method of adding and subtracting integers, and simplifying expressions with addition and subtraction in them. A zero pair is any pair of numbers that when added or subtracted, equal zero. Based on this definition, the only numbers that can form a zero pair, besides two zeros, are a negative number n and a positive number n. When in equations, zero pairs can be cancelled out, therefore simplifying the expression. This is very useful when more complicated equations are given.

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A detailed tutorial on identifying zero polynomials. Step by step tutorial including several examples of identifying zero polynomials for reference.

A zero polynomial is the additive identity of an additive group of polynomials. So this means it is not a unique polynomial, even though it may seem like it. In order to identify a zero polynomial, you need to be aware of the two properties that zero polynomials possess. The first one is that all coefficients of a zero polynomial are zero, and add up to zero. The second is that a zero polynomial doesn’t have a degree – it is an undefined degree. Typically people will write this as a degree of -1, or more common, of negative infinity.

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A detailed tutorial on the identity matrix. Step by step tutorial including several examples of the identity matrix and how to solve it for reference.

An indentity matrix is a matrix that is said to be of size n. It is considered to be the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. The identity matrix is denoted as the variable I. The identity matrix has some extremely important properties of its own, especially multiplication properties. It is a unique type of matrix that is found rarely, but is used very often in several different branches of math.

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A detailed tutorial on upper and lower triangular matrices. Step by step tutorial including several examples of triangular matrices for reference.

A triangular matrix is a kind of square matrix where an element above or below the main diagonal is 0. This gives the true elements of the matrix a triangle shape, which is how it got its name. An upper triangular matrix is sometimes called a right triangular matrix. The matrix is up in the right upper corner, and the 0 element is in the lower left corner. A lower triangular matrix is sometimes called a left triangular matrix. The matrix is in the left bottom corner, and the 0 element is in the upper right corner.

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A detailed tutorial on scalar triple products. Step by step tutorial  including several examples of scalar triple products for reference.

A scalar triple product is a way of applying other multiplication operators to three vectors. Quite often, the scalar triple product is denoted as (a, b, c). It can also be defined as (a b c) = a(b x c). The scalar triple product has three main properties. The first one is that the absolute value of the scalar triple product is the volume of the three dimensional figure that is formed by the three vectors. The second one is the scalar triple product is only zero if the three vectors are linearly independent. The three vectors must lie in the same plane for this to be true. The third one is that the scalar triple product is only positive if all three of the vectors are considered right-handed.

A simple way to write the scalar triple product is to line up the coordinates of the vectors in this form: This is the same as saying

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A detailed tutorial on the definition of a null vector. Step by step tutorial including several examples of null vectors for reference.

A null vector is a vector that has no direction. It is placed at the coordinates (0, 0, 0) in Euclidean space. Another name for a null vector is a zero vector. Although the null vector is the only vector that has no direction, we cannot say that the null vector is unique because more than one vector has the possibility of being null.

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A detailed tutorial on the conjugate zeros theorem. Step by step tutorial including several examples of the conjugate zeros theorem for reference.

The conjugate zeros theorem states that if a + b * i is a zero of a polynomial with real coefficients, then so is a – b * i. The conjugate zeros theorem can be proved by taking any function in this form and setting it equal to zero. The conjugate zeros theorem makes many equations easier to solve, especially complex equations when you get to higher levels of math.