Solve for x . | x-6 3 -2 x+1 |=0 |...

Name: Problem 46, Chapter 3: Elementary Linear Algebra
Uploaded: 2022-02-05T19:37:36-08:00
Duration: 4 min 49 s
Channel: Asif Khan
Description: Solve for x . | x-6 3 -2 x+1 |=0

Key Concepts

Determinant of a 2x2 Matrix

In linear algebra, the determinant of a 2x2 matrix is a scalar value computed from its elements. It is calculated by multiplying the elements on the main diagonal and then subtracting the product of the elements on the off-diagonal. This concept is fundamental as it informs properties such as invertibility of the matrix.

Quadratic Equation

Expanding the determinant of a 2x2 matrix often leads to a quadratic equation—a second-degree polynomial equation. Solving such equations involves methods like factoring, completing the square, or applying the quadratic formula, which are essential techniques in algebra.

Zero Product Property

The zero product property states that if a product of factors equals zero, then at least one of the factors must be zero. This property is crucial in solving factored quadratic equations, as it allows one to set each factor equal to zero to identify the solutions.

Transcript

00:01 Hi, today in this video we will learn to solve for a variable x when we are given a determinant which is having the entries like this one x minus 6 the first entry and then the second entry in row 1 is 3 and then the second row is having minus 2 and x plus 1 and given that this determinant is equals to 0 and we have to solve for x simply solve for x simply means here we have to find the value of x for which this determinant will be equal to 0 and we know that and 2 by 2 this is the determinant this determinant is of 2 by 2 matrix and for 2 by 2 matrix i will give you an example like how to expand the determinant if we have a matrix like a b and c d this is a matrix this is a matrix and a then determine let's say this is matrix c then determinant of c is simply we know that we can write this in determinant form a b c and d like this one and we can find the determinant by simply multiplying the main diagonal increase and then like this one a multiply by b and then there will be sign of subtraction and then we will multiply the secondary diagonal entries this one b multiply by c in this way we can find a b minus b c which is simply the determinant of this matrix c so the same concept of finding a determinant of 2 by 2 matrix i will use here in our case so here i can write this is first i will multiply the entries on diagonal main diagonal or principal diagonal that is it would be like this one x minus 6 into x plus 1 and then there will be sign of subduction and then the scantra diagonal entries will be multiplied together these two and a minus 3 like this one minus 2 and 3 then if that's equal to 0 as well so now we can find, we can solve further one step you can see here.

02:37 That would be simply x.

02:39 I will take this x and then i will multiply with the next all value x plus 1.

02:44 And then i will take this minus 6...

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