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- 1. lecture 5 Assist. Lect.Hiba Abdul –Kareem
- 2. Matrices • A groupof numbers (called elements)arranged in rows and columns and enclosed in brackets.
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- 4. Dimension or sizeof matrices • A matrix with m rows and n columns is called a matrix of order m x n or a m x n matrix
- 5. Dimension or sizeof matrices
- 6. TYPES OF MATRICES 1.Column Matrix: An m x n matrix is called row matrix if n = 1.
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- 16. OPERATIONS ON MATRICES ADDITIONAND SUBTRACTION • Two matrices may be added (or subtracted) if they are the same order. • Simply add (or subtract) the corresponding elements. So, A + B = C
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- 35. The determinant ofmatrix • The determinant of a matrix is a scalar value that is used in many matrix operations. The matrix must be square (equal number of columns and rows) to have a determinant. The notation for absolute value is used to indicate "the determinant of", e.g. 𝑨 means "the determinant of matrix A" and 𝑎 𝑏 𝑐 𝑑 means to take the determinant of the enclosed matrix. Methods for finding the determinant vary depending on the size of the matrix.
- 36. The determinant ofmatrix • The determinant of a 2×2 matrix is simply: • where 𝐴 = 𝑎 𝑏 𝑐 𝑑 , • det(A) = A = a b c d = ad – bc • Example (1): • |A| = 2 x 8 – 4 x 3 = 16 – 12 = 4
- 37. The determinant ofmatrix Example (2): Example (3):
- 38. The determinant ofmatrix • The determinant of a 3×3 matrix can be calculated by repeating the first two columns as shown below. 𝐀 = a11a22a33 + a12a23a31 + a13a21a32 - a13a22a31 - a11a23a32 - a12a21a33
- 39. The determinant ofmatrix • he determinant of a 3×3 matrix can be calculated by the following process: • 𝐀 = 𝐚𝟏𝟏 𝐚𝟏𝟐 𝐚𝟏𝟑 𝐚𝟐𝟏 𝐚𝟐𝟐 𝐚𝟐𝟑 𝐚𝟑𝟏 𝐚𝟑𝟐 𝐚𝟑𝟑 • 𝐀 = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)
- 41. The determinant ofmatrix
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- 45. Question 2 • Findthe value of x – y, if
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- 51. Question 8 • Ifa matrix has 5 elements, then write all possible orders it can have
- 52. Question 9 • Ifa matrix has 5 elements, then write all possible orders it can have
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