# Matrix Help: Understanding Parts (a) to (d)

• shermaine80
In summary, the student is trying to figure out how to do part c and part d for an equation, but is having difficulty understanding what is being asked. The first equation in part c is 5x+ 5y- 10z= 0 which can be written as 5x+ 5y- 10z+ 0w= 0 to include w, and the first equation in part d is w has moved to the top of the array which means it will be multiplied by the first column of the matrix B.
shermaine80
Hi Guys,

I need help. I try out part(a) and (b).But it seem to me...my answer is not correct or too brief. Can anyone assist me? As for part (c). I'm not sure what A means here. Is it referring to A = [ cost -sint
sint cost]?
And what abt part (d), what does B means here? Can someone assist me how to do part (c) and (d)? Please advise. Thanks.

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What exactly is your problem? You should state it out more clear. I looked at the attachments and still didn't understand what you mean. Everything looks very clear.

For part a, have you considered multiplying the matrix you are given by the square of A?
As for c, A is simply the matrix of coefficients from the three equations which you are given in the question. The A in the equation does not refer to the A in the first part. Once you have A, find the inverse.
Part d, is almost the same as part c (but with a few changes).

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Hi,

Is it possible to work out part (c) and (d) for me?

If you've seen any examples of changing systems of equations to matrix equations, c and d should be easy.

The first equation in c is 5x+ 5y- 10z= 0 which you can also write as 5x+ 5y- 10z+ 0w= 0 in order to include w. Remembering that you multiply matrices by multiplying "row times column", the first row of matrix A must be [5 5 -10 0] so that
$$\left[\begin{array}{cccc}5 & 5 & -10 & 0\end{array}\right]\left[\begin{array}{c}x \\ y \\ z \\ w\end{array}\right]= 5x+ 5y- 10z+ 0w$$

For part d, all that is different is that w has moved to the top of the array. That means it will be multiplied by the first column of the matrix B.

As far as part a is concerned, I would just multiply A10, which is given, by A twice more! I suspect you will need to use the "sum" formulas for sin(x+ y) and cos(x+y).

In b, (i), you say "there will be a solution if they intersect", iii, "multiple solution if they coincide", and for iv (I can't read the last part of ii) "no solution if the lines are parallel"

If what intersect? There certainly are no "lines" because this is not a two dimensional problem. You may be thinking of this as representing n "hyperplanes" but that is not given. The question is asking about the conditions on A and b.

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## What is "Matrix help"?

"Matrix help" refers to assistance or support with understanding and working with matrices, which are mathematical structures consisting of rows and columns of numbers. Matrices are commonly used in fields such as physics, engineering, and computer science.

## Why do I need to know about matrices?

Matrices are powerful tools for representing and manipulating data, equations, and transformations. They have many practical applications in fields such as data analysis, computer graphics, and machine learning. Understanding matrices can greatly enhance your problem-solving abilities and broaden your understanding of mathematics and its applications.

## How do I add or multiply matrices?

Adding and multiplying matrices involves following specific rules and operations. To add two matrices, they must have the same dimensions, and you simply add the corresponding entries in each matrix. To multiply two matrices, the number of columns in the first matrix must match the number of rows in the second matrix, and the resulting matrix will have the same number of rows as the first and the same number of columns as the second. The entries in the resulting matrix are calculated by multiplying and then adding specific entries from the two original matrices. It is important to carefully check the dimensions of the matrices and follow the rules for addition and multiplication to correctly perform these operations.

## Can matrices be inverted?

Some matrices can be inverted, meaning that a matrix can be multiplied by its inverse to give the identity matrix (a matrix with 1s on the main diagonal and 0s everywhere else). The inverse of a matrix is only defined for square matrices (matrices with the same number of rows and columns) that are nonsingular (meaning they have a nonzero determinant). The process of finding the inverse of a matrix involves complex mathematical calculations and is typically done using software or calculators.

## How can I use matrices in real-world problems?

Matrices can be applied to a wide range of problems in various fields. For example, in physics, matrices can be used to represent linear transformations such as rotations and reflections. In economics, matrices can be used to model and solve systems of equations representing supply and demand. In computer science, matrices are used in image processing and computer graphics. By understanding how to use matrices, you can apply them to solve real-world problems in your field of study or interest.

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