 ## Tutoring on Matrix Operations

Learning Objectives:

#### Understand and Apply Matrix Operations: Additon, Subtarction,

Math Tutoring on Matrix Operations

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 ith row of the first matrix by the corresponding element in the jth column of the second matrix. The sum of these products will be the element aij in the product. It is important to note that Matrix multiplication is not commutative, so the order of multiplication is very important, AB ≠ BA.

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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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