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Matrices and Determinants

Matrices and Determinants. Lecture May 2011. Mathematics XI 2011. 1.1 Matrices. Zero matrices. Every element of a matrix is zero, it is called a zero matrix, i.e.,. 1.2 Operations of matrices. Sums of matrices.

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Matrices and Determinants

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  1. Matrices and Determinants Lecture May 2011 Mathematics XI 2011

  2. 1.1 Matrices Zero matrices • Every element of a matrix is zero, it is called a zero matrix, i.e.,

  3. 1.2 Operations of matrices Sums of matrices • Two matrices of the same order are said to be conformable for addition or subtraction. • Two matrices of different orders cannot be added or subtracted, e.g., are NOT conformable for addition or subtraction.

  4. 1.3 Types of matrices • Identity matrix • The inverse of a matrix • The transpose of a matrix • Symmetric matrix • Orthogonal matrix

  5. 1.4 Properties of matrix • (AB)-1 = B-1A-1 • (AT)T = A and (lA)T = l AT • (A + B)T = AT + BT • (AB)T = BT AT

  6. 1.5 Determinants Determinant of order 2 Consider a 22 matrix: • Determinant of A, denoted , is a number and can be evaluated by

  7. 1.6 Inverse of a 33 matrix Cofactor matrix of The cofactor for each element of matrix A:

  8. 1.6 Inverse of a 33 matrix Cofactor matrix of is then given by:

  9. 1.6 Inverse of a 33 matrix Inverse matrix of is given by:

  10. 1.7 Applications • Cement SteelFloor(sq.ft) • Banglow 200 Yds30025002000 • Banglow 300 Yds50035003000 • Banglow 500 Yds75050005500 • KhiLhrIsl • 450375520 • 330350410 • 12090150 • Total Cost • KhiLhrIsl • Banglow 200 Yds120000011675001481000 • Banglow 300 Yds174000016825002145000 • Banglow 500 Yds264750025262503265000

  11. Students can also create parallel examples in • Financial institution • Industries • Time management

  12. By : Syed Shujaat Hussain • Special Thanks to My Master Trainer Mr. AdnanKiyani

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