Applied Maths Lecture Notes

Overview

• Lecture focuses on using Excel for matrix and determinant operations
• Operations covered: addition, subtraction, multiplication, transpose, determinant, and inverse of matrices
• Applicable for CBSE Class 12 Applied Maths and enrichment for Pure Maths students

Matrix Operations in Excel

Adding Matrices

1. Matrix A (2x3):

   • Values:
     | 2 | 3 | -1 |
     | 3 | 4 | 1 |

2. Matrix B (2x3):

   • Values:
     | 1 | -1 | 2 |
     | 3 | 1 | 2 |

3. Formula for A + B:

   • Select the 2x3 area for result
   • Enter formula: =A+B
   • Press Ctrl + Shift + Enter

4. A - B:

   • Same process as addition, but use - instead of +

5. Scalar Multiplication (e.g., 2A + 3B):

   • Select area, enter: =2*A + 3*B, then Ctrl + Shift + Enter

Multiplying Matrices

1. Matrix A (2x3) and Matrix B (3x2):

   • A:
     | 2 | -1 | 3 |
     | 3 | 2 | 4 |
   • B:
     | 2 | -4 |
     | 1 | -1 |
     | 3 | 2 |

2. Resulting Matrix will be (2x2):

   • Select 2x2 area
   • Use formula: =MMULT(A, B) and Ctrl + Shift + Enter

3. Multiplying B and A will yield a (3x3) matrix:

   • Select 3x3 area, use: =MMULT(B, A), then Ctrl + Shift + Enter

Finding Determinants

1. Determinant of Matrix A:

   • Use formula: =MDETERM(A) and Ctrl + Shift + Enter
   • Result: 0

2. Determinant of Matrix B:

   • Same steps as for A

3. Determinant of AB:

   • Confirm: =MDETERM(MMULT(A,B))
   • Result should also be 0

Finding Inverse of a Matrix

1. Matrix A (3x3):

   • Values:
     | 3 | 4 | 2 |
     | 0 | 2 | -3 |
     | 1 | 1 | -2 |

2. Check Determinant:

   • If determinant is not 0, inverse exists

3. Finding Inverse:

   • Select 3x3 area, use formula: =MINVERSE(A), then Ctrl + Shift + Enter

Transpose of a Matrix

1. Matrix A (2x3) and Matrix B (3x2):

   • A values:
     | 3 | -1 | 3 |
     | 2 | -4 | 6 |
   • B values:
     | -1 | 6 | -7 |

2. Transpose:

   • For A: Select 3x2 area, use: =TRANSPOSE(A) and Ctrl + Shift + Enter
   • For B: Select 2x3 area, use: =TRANSPOSE(B) and Ctrl + Shift + Enter

Conclusion

• Various operations demonstrated: addition, subtraction, scalar multiplication, multiplication, determinant, inverse, and transpose
• Video serves as a practical guide, useful for Class 12 students

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