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RD Sharma Solutions for Class 12 Maths Chapter 5, Algebra of Matrices, , , , PAGE NO: 5.6, , 1. If a matrix has 8 elements, what are the possible orders it can have? What if it has 5, elements?, , Solution:, , If a matrix is of order m x n elements, it has m n elements. So, if the matrix has 8, elements, we will find the ordered pairs m and n., , mn=8, , Then, ordered pairs m and n will be, , m x n be (8 x 1),(1 « 8),(4 x 2),(2 x 4), , Now, if it has 5 elements, , Possible orders are (5 x 1), (1 x 5)., , 23 -5 25-1, 21f A=(ayj]=|1 4 4 and B = (bij) = - ‘| then find, 07 -2 1 2, (i)ax + ba, (ii) ayy by; + azab29, Solution:, (i), We know that, ay, ay ", A= [ay] = an an ay}... (i), a3, a2 ay, , , , bu bye, , Aral Bos lon ba ee, ba, b32, , Also given that, , Corn, Ne Oo, , -5 2 -1, 9} and B=[bj)=|-3 4, 2 1 2, , Now, Comparing with equation (1) and (2), a22 = 4 and by, =-3, ax + by =4+(-3)=1, , a-tal=|, , , , JCC Fazilnagar

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RD Sharma Solutions for Class 12 Maths Chapter 5, , , , Algebra of Matrices, (ii), We know that, a, 42 a3, A = [aij] = Jan ax a3} .....(i), az aR ay, bu bya, And B= |by, by} ..... (it), ba, bag, Also given that, 23 -5 2 =-1, A=|ajj)=]1 4 9] andB=(bj)=|-3 4, 07 -2 1 2, , Now, Comparing with equation (1) and (2), an = 2, a2 = 4, bi = 2, ba» =4, 411 bi; + a2? bx22 =2*%24+4x4=4+4+16=20, , 3. Let A be a matrix of order 3 x 4. If R; denotes the first row of A and C, denotes its, second column, then determine the orders of matrices R; and C)., , Solution:, Given A be a matrix of order 3 x 4., So, A = [a))] 3x4, Ri = first row of A = [aai, a:2, a13, axa), So, order of matrix Ri=1x 4, C, = second column of, a12, A= lan, a32, , Therefore order of C, = 3x1, , 4. Construct a 2 x3 matrix A = [a)|] whose elements aj are given by:, , (i) aj=ixj, (ii) aij= 2i-j, (iii) a,j=i+j, , (iv) aj; = (i + j)?/2, , , , JCC Fazilnagar