# 311.1.4.6 create a vector equation

• MHB
• karush
In summary, the conversation discusses how to multiply a matrix with a vector and provides two different approaches to solve the problem. The first approach involves multiplying each element in the matrix by the corresponding element in the vector and then adding the results. The second approach involves distributing the vector and then adding the results. The conversation also mentions using macros on Overleaf and the possibility of plotting the problem on demos.
karush
Gold Member
MHB

#6

$$\left[\begin{array}{rrr} 2&-3\\ 3&2\\ 8&-5\\ -2&1 \end{array}\right] \left[\begin{array}{rrr} -3\\5 \end{array}\right] =\left[\begin{array}{rrrrr} -21\\1\\-49\\11 \end{array}\right]$$
do they want $x_1[ ]+x_2[ ]+x_3[ ]+x_4[ ]$
cant seen to find example for this

$$\left[\begin{array}{rl} 2\cdot (-3)&+(-3)\cdot 5\\ 3\cdot (-3)&+2\cdot 5\\ 8\cdot (-3)&+(-5)\cdot 5\\ -2\cdot (-3)&+1\cdot 5 \end{array}\right ] =\left[\begin{array}{rl} -6&-15\\ -9&+10\\ -24&+25\\ 6&+5 \end{array}\right]$$

or
$$-3\left[\begin{array}{r} 2\\3\\8\\-2 \end{array}\right] +5\left[\begin{array}{r} -3\\2\\-5\\1 \end{array}\right] =\left[\begin{array}{rrrrr} -21\\1\\-49\\11 \end{array}\right]$$

ok this is #8 which I did in Overleaf with Macros assume we don't try to solve for $z_?$
just curious can this be ploted on demos?

Last edited:

## 1. What is a vector equation?

A vector equation is an equation that represents a vector in terms of its components. It is typically written in the form of v = ai + bj + ck, where v is the vector, a, b, and c are the components of the vector, and i, j, and k are the unit vectors in the x, y, and z directions, respectively.

## 2. Why is it important to create a vector equation?

Creating a vector equation allows us to represent a vector in a concise and organized manner. It also allows us to easily perform mathematical operations on vectors, such as addition, subtraction, and scalar multiplication.

## 3. How do you create a vector equation?

To create a vector equation, you first need to determine the components of the vector. Then, you can write the equation in the form of v = ai + bj + ck, using the appropriate values for a, b, and c.

## 4. What are some applications of vector equations?

Vector equations are used in many fields, including physics, engineering, and computer graphics. They are especially useful in describing the motion of objects, forces acting on objects, and geometric transformations.

## 5. Can you give an example of a vector equation?

One example of a vector equation is v = 2i + 3j - k, which represents a vector with a magnitude of 2 in the x direction, 3 in the y direction, and -1 in the z direction. This could represent the displacement of an object moving 2 units to the right, 3 units up, and 1 unit down.

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