Identity matrix
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An identity matrix is a square matrix with ones along its main diagonal and zeros elsewhere. When a matrix is multiplied by its corresponding identity matrix, the original matrix is returned. The identity matrix for an n×n matrix is denoted In×n. Some key properties of identity matrices are that AI = IA = A for any square matrix A of the same dimensions.
Identity matrix
- 1. 4.6IDENTITY MATRIXLOH HUI YICHANG WAN LINGLEE CHAI EN KAM SIEW HUEY
- 2. Definition An identity matrix, I, is a matrix which when multiplying it to another matrix, such as A, the product is the matrix A itself.IA = A and AI = AAI = IA = A
- 3. Identity Matrix is also called as Unit Matrix or Elementary Matrix.Identity Matrix is denoted with the letter “In×n”, where n×n represents the order of the matrix.One of the important properties of identity matrix is: A×In×n = A, where A is any square matrix of order n×n.
- 4. A matrix with the same number of rows and columns is called a squarematrix.3x3
- 5. An identity matrix, I, is a square matrix and the elements are 0 and 1 only.The elements in the main diagonal are 1 while the others are 0. 1 0 0 0 1 0 0 0 1I =3 x 3
- 6. EXAMPLE 11 2 1 1 3 7 3 4 1 1 3 7 so 1 1 1 1 is not an identity matrix
- 7. EXAMPLE 21 2 1 0 1 2 3 4 0 1 3 4so 1 0 0 1 is the identity for 2x2 matrices
- 8. EXERCISES1 1 2 1 0 -2 1 0 12 1 0 1 2 0 1 -2 12-2 1 2-2 1
- 10. Solution:Step 1: M = -4 -3 (Given) -6 5Step 2: As M is square matrix of order 2×2, the identity matrix I is also of same order 2×2. (Rule for Matrix Multiplication)Step 3: Then M×I = -4 -3 1 0 -6 5 0 1 = (-4x1)+(-3x0) (-4x0)+(-3x1) (-6x1)+(5x0) (-6x0)+(5x1)(Matrix Multiplication)×
- 11. Step 4: = -4 -3 -6 5 (Simplifying)Step 5: Hence M×I = M = -4 -3 -6 5 #