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Types of Matrices | Maths

Matrices are distinguished on the basis of their order, elements and certain other conditions. There are different types of matrices but the most commonly used are discussed below. Let’s find out the types of matrices in the field of mathematics. Types of Matrices Different types of Matrices and their forms are used for solving numerous problems. 1) Row Matrix A row matrix has only one row but any number of columns. A matrix is said to be a row matrix if it has only one row. For example, A=[−1/2√523] is a row matrix of order 1 × 4. In general, A = [aij]1 × n is a row matrix of order 1 × n. 2) Column Matrix A column matrix has only one column but any number of rows. A matrix is said to be a column matrix if it has only one column. For example, A=⎡⎣⎢⎢⎢0√3−11/2⎤⎦⎥⎥⎥ is a column matrix of order 4 × 1. In general, B = [bij]m × 1 is a column matrix of order m × 1. 3) Square Matrix A square matrix has the number of columns equal to the number of rows. A matrix in which the number of rows is equal to the number of columns is said to be a square matrix. Thus an m × n matrix is said to be a square matrix if m = n and is known as a square matrix of order ‘n’. For example, A=⎡⎣⎢33/24−1√3/2301−1⎤⎦⎥ is a square matrix of order 3. In general, A = [aij] m × m is a square matrix of order m. 4) Rectangular Matrix A matrix is said to be a rectangular matrix if the number of rows is not equal to the number of columns. For example, A=⎡⎣⎢⎢⎢⎢33/247/2−1√3/23201−1−5⎤⎦⎥⎥⎥⎥ is a matrix of the order 4 × 3 5) Diagonal matrix A square matrix B = [bij] m × m is said to be a diagonal matrix if all its non-diagonal elements are zero, which is a matrix B =[bij]m×m is said to be a diagonal matrix if bij = 0, when i ≠ j. For example, A=[4][−1002]⎡⎣⎢3000−50002⎤⎦⎥ are diagonal matrices of order 1, 2, 3, respectively. 6) Scalar Matrix A diagonal matrix is said to be a scalar matrix if all the elements in its principal diagonal are equal to some non-zero constant. A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal, that is, a square matrix B = [bij]n × n is said to be a scalar matrix if bij = 0, when i ≠ j bij = k, when i = j, for some constant k. For example, A=[4][−100−1]⎡⎣⎢300030003⎤⎦⎥ are scalar matrices of order 1, 2 and 3, respectively. 7) Zero or Null Matrix A matrix is said to be zero matrix or null matrix if all its elements are zero. For Example, A=[0][0000]⎡⎣⎢000000000⎤⎦⎥ are all zero matrices of the order 1, 2 and 3 respectively. We denote the zero matrices by O. 8) Unit or Identity Matrix If a square matrix has all elements 0 and each diagonal elements are non-zero, it is called identity matrix and denoted by I. Equal Matrices: Two matrices are said to be equal if they are of the same order and if their corresponding elements are equal to the square matrix A = [aij]n × n is an identity matrix if aij = 1 if i = j aij = 0 if i ≠ j We denote the identity matrix of order n by In. When the order is clear from the context, we simply write it as I. For example, A=[1][1001]⎡⎣⎢100010001⎤⎦⎥ are identity matrices of order 1, 2 and 3, respectively. Observe that a scalar matrix is an identity matrix when k = 1. But every identity matrix is clearly a scalar matrix. 9) Upper Triangular Matrix A square matrix in which all the elements below the diagonal are zero is known as the upper triangular matrix. For example, A=⎡⎣⎢300−540709⎤⎦⎥ 10) Lower Triangular Matrix A square matrix in which all the elements above the diagonal are zero is known as the upper triangular matrix. For example, A=⎡⎣⎢30−5047009⎤⎦⎥ #matrice #typesofmatrices #matrices For more videos, online classes, 24X7 Doubts solving and Mock tests, Visit Toppr - The better learning app. #BetterLearning on the Toppr app, download now Google Play: http://bit.ly/2vRBqcb App Store: http://apple.co/2vpRAr9 Website: https://www.toppr.com/ Download Doubts on Chat App: Android Play Store: http://bit.ly/2B6w7oy iOS App Store: http://apple.co/2ziAA75 Facebook:   / beingtoppr   Twitter:   / mytoppr   Instagram:   / mytoppr   LinkedIn:   / toppr-com