Algebra instructions

To get started with elements of linear algebra, you first need to see how vectors and arrays are defined in CalcMe. You can define vectors in three different ways: by using the vector command, using the icon you can find in the Linear Algebra section of the Menu, or by typing it manually. The last two are the most common.

 

You can also define vectors as variables, perform basic operations between them, and access specific elements.

On the other hand, you have only two options if you want to define a matrix, but they are more than enough. You can use the icon next to the vector in Linear Algebra or enter it manually as a vector of vectors.

Additionally, once the matrix is created, you can resize it by inserting or removing rows and columns with more icons you can find in the Menu.

Finally, as with vectors, you can also perform basic operations between matrices and access their elements.

Apart from the basic operations already seen as the sum of matrices or the product of a matrix and a scalar, CalcMe allows you to perform a wide range of actions given a set of matrices. First, the product between matrices.

Continuing with classical operations with matrices, you can also find commands in the Linear Algebra section of the Menu that allows you to calculate the determinant, inverse, and transpose of a given matrix. In the same way, you can also easily create an identity matrix of the dimension you want.

Finally, you can find the range, kernel, and matrix image by using the corresponding commands.

Given two bases of a vector space , in our case and , the matrix whose columns correspond to the coordinates of the vectors of in the base , is called the matrix of the change of base from to . CalcMe allows you to find this matrix and, consequently, the vector coordinates of in the base .

To create a straight line, you need to specify a point on the line and the direction it will follow (i.e., its slope). With these ingredients (though they aren't the only possible ones) and the line command, you can easily create and represent a straight line in the plane.

You can extend these actions into space with similar syntax and create and render a 3-D straight line. Notice that the line appears as an intersection of two planes.

On the other hand, you will need a point and two director vectors to create a plane. With these ingredients (though they aren't the only possible ones) and the plane command, you can create and render a plane in the space.

Translating is a transformation that moves objects without causing them to deform since each point of the object is moved in the same direction and at the same distance. Set the translation distance (both on the axis and the axis) to define it.

In fact, you can apply this transformation to more complex objects than points.

Suppose you apply a rotation to a point , its position changes following a circular trajectory in the plane. In order to define it, you must set the rotation angle and the pivot or rotation point. CalcMe will interpret the pivot as the origin if you don't indicate it.

As you have seen before, you can apply this transformation to more complex objects than points.

Or specifying another rotation point different from the origin.

Scaling a point using a fixed point , implies multiplying by some factors the horizontal and vertical distances between and . If you don't indicate it, CalcMe will interpret that the point is the origin.

As you have seen before, you can apply this transformation to a more complex object.

Or by specifying another fixed point other than the origin. In this case, you will need to start by applying a translation so that the fixed point matches the coordinate origin. Once you've made a move, you have to finally apply the scaling to undo the translation.