Matrices and quadratic basics help

In summary, the conversation discusses finding the value of k in a quadratic equation by expanding a matrix multiplication and collecting terms. The correct value of k is -8, which was found by comparing the given equation with the one obtained from the matrix multiplication. The person seeking help also expresses gratitude for the explanation and acknowledges their mistake.
  • #1
Taylor_1989
402
14
I have figured out the answer to the question, but I have no idea why and how it works.

I have attached a copy of the question. I do apologize I am still having trouble putting into latex, I can install some but not all, so bare with me.

So if I multiple out the matrices I get [itex]\chi[/itex]2 + 10[itex]\rightarrow[/itex] I then minus this from the quadratic [itex]\chi[/itex]2 + 8[itex]\chi[/itex] + 10 = 0 [itex]\rightarrow[/itex] Which then gives me 8[itex]\chi[/itex] = 0

reagrange and I have [itex]\chi[/itex] = -8

Which is the right answer, I checked the mark scheme but I am suppose to find the value of K and not x. This make me think I have done the wrong maths but got the right answer.

Could someone point out if I have gone wrong, it would be very helpful.

It is the one highlighted.
 

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  • #2
Hey Taylor_1989 and welcome to the forums.

Expanding your equation gives x^2 + 10 = kx which implies x^2 - kx + 10 = 0. But we know the equation is x^2 + 8x + 10 = 0 which means -k = 8 so k = -8.

Remember you know the equation, and you are finding the value of k when you expand your matrix multiplication and collect terms: solving for x is finding the roots of the function where you are solving x^2 + 8x + 10 = 0 for the variable x.
 
  • #3
chiro said:
Hey Taylor_1989 and welcome to the forums.

Expanding your equation gives x^2 + 10 = kx which implies x^2 - kx + 10 = 0. But we know the equation is x^2 + 8x + 10 = 0 which means -k = 8 so k = -8.

Remember you know the equation, and you are finding the value of k when you expand your matrix multiplication and collect terms: solving for x is finding the roots of the function where you are solving x^2 + 8x + 10 = 0 for the variable x.

Thanks for the help, for some reason I got my equations mixed up, it nevered occurred to me to put Kx into a quadratic and then compare. I should have spotted it really. Well learn by your mistakes. Once again many thanks
 

1. What is a matrix?

A matrix is a rectangular array of numbers or variables arranged in rows and columns. It is typically represented by a capital letter and can be used to represent data or perform mathematical operations.

2. What is the difference between a square matrix and a non-square matrix?

A square matrix has the same number of rows and columns, while a non-square matrix has a different number of rows and columns. Square matrices are used in certain operations, such as finding the determinant or inverse, that do not apply to non-square matrices.

3. How do you add or subtract matrices?

To add or subtract matrices, the matrices must have the same dimensions (same number of rows and columns). Simply add or subtract the corresponding elements in each matrix to get the resulting matrix.

4. How do you multiply matrices?

To multiply two matrices, the number of columns in the first matrix must match the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. The elements of the resulting matrix are found by multiplying corresponding elements from the first matrix and second matrix, and then adding them together.

5. What are quadratic equations and how do you solve them?

A quadratic equation is a polynomial with a degree of 2, meaning it has an x2 term. It is typically written in the form ax2 + bx + c = 0. To solve a quadratic equation, you can use the quadratic formula (x = (-b ± √(b2 - 4ac)) / 2a) or factor the equation and solve for the values of x.

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