Linear Algebra Trivia Quiz

Explanation
A linear expression is a mathematical expression that consists of variables, coefficients, and operators such as addition, subtraction, and multiplication. It does not contain an equality sign. On the other hand, a linear equation is a mathematical statement that includes an equality sign and represents a relationship between two linear expressions. Therefore, the presence of an equality sign is what differentiates a linear expression from a linear equation.

Explanation
The number attached to the alphabet is called a coefficient. In mathematics, a coefficient is a numerical or constant factor that is multiplied by a variable in an algebraic expression. It determines the scale or magnitude of the variable's effect in the expression. Therefore, the correct answer is coefficient.

Explanation
In Linear Algebra, alphabets are referred to as variables. Variables are used to represent unknown values or quantities in mathematical equations or expressions. They are typically represented by letters from the alphabet and can take on different values. In the context of Linear Algebra, variables are often used to represent the unknowns in systems of linear equations or to denote the parameters in matrices and vectors.

Explanation
An identity is a term given to an equation that is true for all values of the variable. It represents a statement that holds true regardless of the specific values of the variables involved. In other words, an identity is always true, no matter what values are substituted into the equation.

Explanation
A quadratic function has a parabolic graph. This is because a quadratic function is a polynomial function of degree 2, and the graph of a quadratic function is always a parabola. A parabola is a U-shaped curve that can open upwards or downwards, depending on the coefficients of the quadratic function. The graph of a quadratic function is symmetric about its vertex, and it can have a maximum or minimum point depending on the leading coefficient. Therefore, the correct answer is "Parabolic."

Explanation
"Rhetorical" is not a stage of Algebra. Algebra typically involves stages such as Analytical, Syncopated, and Symbolic, which deal with mathematical symbols, equations, and problem-solving techniques. "Rhetorical" does not have a direct connection to the stages of algebra but may be used in a broader context to describe the communication or explanation of algebraic concepts.

Explanation
There are three stages of Algebra. Algebra 1 is typically taught in middle school or early high school and covers basic concepts such as linear equations and graphing. Algebra 2 is usually taught in later high school years and delves deeper into topics like quadratic equations and exponential functions. Lastly, there is Advanced Algebra, which is a more advanced level of the subject and is often taught at the college level.

Explanation
Determinants were used as the first systematic way to solve linear algebra problems. Determinants are mathematical objects that can be calculated for square matrices and provide valuable information about the matrix, such as whether it is invertible or singular. They were introduced by mathematician Gabriel Cramer in the 18th century and have since become an essential tool in linear algebra. By using determinants, mathematicians were able to develop a systematic approach to solving systems of linear equations and studying properties of matrices.

Explanation
Hermann Grassmann is the correct answer because he published the theory of extension.

Explanation
The Latin meaning of the word "matrix" is "womb." In Latin, "matrix" refers to the female reproductive organ where a fetus develops. This term is often used metaphorically to describe something that serves as a nurturing or creative source, similar to how a womb nurtures and creates life. Therefore, "womb" is the correct answer in this context.