That's not what happened. Try multiplying out the left hand expression of the second line of 4.13.kristo said:
Linear algebra is a branch of mathematics that deals with the study of vector spaces and linear transformations. It involves the use of mathematical structures such as matrices and systems of linear equations to solve problems in various fields such as physics, engineering, and economics.
A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and x is a variable. It is a type of polynomial function that has a degree of 2 and is commonly used to model relationships between variables in real-world problems.
A unique minimizer of a quadratic function is the value of x that minimizes the function and is the only solution to the equation f'(x) = 0. In other words, it is the point where the slope of the quadratic function is equal to 0, and it represents the lowest point on the graph of the function.
Linear algebra techniques, such as matrix operations and solving systems of linear equations, can be used to find the unique minimizer of a quadratic function. By setting the derivative of the function equal to 0 and using linear algebra methods, we can solve for the value of x that minimizes the function.
Finding the unique minimizer of a quadratic function using linear algebra can have various applications in fields such as economics, physics, and engineering. It can be used to optimize processes and systems, such as finding the minimum cost or maximum profit, and to solve real-world problems involving relationships between variables.