Learning Objectives:

__Math Tutoring on Matrix Operations__

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**Matrix Operation** includes **Matrix Addition, Subtraction, Scalar Multiplication, Translation and Dilation. **

The sum and difference of two **matrices **can only be found if both **matrices** have the same dimension. To determine the sum, we have to add corresponding elements and for finding the difference we have to subtract corresponding elements. The product of a **scalar** or real number and a **matrix** is equal to the scalar times each element in the **matrix. **

Two important steps in **Matrix Multiplication **are:

**1)** The product of an **(m x n) matrix** and an **(n x k) matrix** is an **(m x k) matrix**. Notice the number of columns in the first **matrix** must be the same as the number of rows in the second **matrix**. If this is not true, the two **matrices **cannot be multiplied.

**2)** To determine each element in the product, multiply each element in the **i**th **row** of the first **matrix** by the corresponding element in the **j**th **column** of the second **matrix.** The sum of these products will be the **element a _{ij}** in the product. It is important to note that

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**Hook Questions:**

*1. How can you use Matrix operations in Transformations like Translation and Dilation?*

*2. Is it possible to do matrix multiplication between any two matrices?*

*3. What is Identity Matrix?*

*4. What is Elementary Matrix?*

*5. Give the difference between Lower and Upper Triangular Matrices.*

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