FINAL

For a 2x2 matrix \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), the determinant is calculated as \( ad - bc \).

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The element at position (i,j) in the resulting matrix is the dot product of the i-th row of the first matrix and the j-th column of the second matrix.

The quadratic formula is used to find the solutions of a quadratic equation \( ax^2 + bx + c = 0 \). It is given by \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

The sum of two numbers is the result of adding them together. For example, the sum of 3 and 5 is 8.

The product of two numbers is the result of multiplying them together. For example, the product of 4 and 5 is 20.

To solve a quadratic equation by factoring, express it in the form \( (x - p)(x - q) = 0 \) and then set each factor to zero: \( x - p = 0 \) or \( x - q = 0 \).

A scalar is a quantity that has only magnitude (e.g., temperature), while a vector has both magnitude and direction (e.g., velocity).

The area of a triangle is given by the formula \( A = \frac{1}{2} \times base \times height \).

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): \( c^2 = a^2 + b^2 \).

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form \( ax + b = 0 \).