Linear Algebra Symbols Solved Examples

Example 1: Find the sum of the two vectors [Tex]\overrightarrow{\rm A}[/Tex]= 3i + 4j + 5k and [Tex]\overrightarrow{\rm B}[/Tex]= -i + 2j + ?

Solution:

[Tex]\overrightarrow{\rm A} + \overrightarrow{\rm B}[/Tex]= (3-1)i + (2 + 4)j + (5 + 1)k = 2i + 6j + 6k

Example 2: Find the sum of the two matrices

[Tex] \begin{bmatrix} 3 & 3\\ 4 & 6\\ \end{bmatrix} and \begin{bmatrix} 1 &-2 \\ 3 & 4 \end{bmatrix}[/Tex] ?

Solution:

Let the two matrices be P = [Tex]\begin{bmatrix} 3 & 3\\ 4 & 6\\ \end{bmatrix}[/Tex]

Q = [Tex]\begin{bmatrix} 1 &-2 \\ 3 & 4 \end{bmatrix}[/Tex]

S = P + Q = [Tex]\begin{bmatrix} 3 & 3\\ 4 & 6\\ \end{bmatrix} + \begin{bmatrix} 1 &-2 \\ 3 & 4 \end{bmatrix} = \begin{bmatrix} 4 & 1\\ 7& 10\\ \end{bmatrix}[/Tex]

Example 3: For the equation 2x – 3 = 2, Solve for x ?

Solution:

6x – 3 = 2

⇒ 6x = 2 + 3

⇒ 6x = 5

⇒ x = 5 / 6 = 0.83

Example 4: Find the inersection of both A = {2, 3, 4}, B = {2, 4, 6,9,11}

Solution:

A = {2, 3, 4}, B = {2, 4, 6,9,11}

Then A ⋂ B = {2, 4}

Example 5: Given two values A = 5 and B = 20, Find the product of A and B

Solution:

Product of A and B = A × B = 5 × 20 = 100

Example 6: If the set A={3,5,7,9} then find n(A) ?

Solution:

n(A) denotes the number of elements in a given set, A={3,5,7,9} then n(A) = 4

Linear Algebra Symbols are mainly focused on comprehending how various systems of linear equations behave and may be solved. This is performed by storing the equations in matrices and vectors, both of which are mathematical objects that may be handled in several ways.

In this article, we will learn about Linear Algebra Symbols their definition and meaning, and others in detail.