### Matrices Class 10th Mathematics Tamilnadu Board Solution

##### Question 1.Which one of the following statements is not true?A. A scalar matrix is a square matrixB. A diagonal matrix is a square matrixC. A scalar matrix is a diagonal matrixD. A diagonal matrix is a scalar matrix.Answer:In the above question we see the following terms,Scalar Matrix, Square Matrix, Diagonal MatrixTo answer this question, we have to know the definition of the above terms.Square Matrix:If the rows and columns of the matrices are equal then it will constitute square like structure. So, it is called as square matrix.E.g. Diagonal Matrix:In a square matrix all the elements are zero except the diagonal elements of the matrix. Then that matrix is said to be diagonal matrix.E.g. Scalar Matrix:In a diagonal matrix, if all the diagonal elements are same then that matrix is said to be a scalar matrix.E.g. Option(A):A scalar matrix should be a square matrix so, it is trueOption(B):Diagonal matrix forms only with the square matrix so, it is trueOption(C):A scalar matrix consists of zero except the diagonal elements so it is true.Option(D):A scalar matrix should comprise of same diagonal elements but in diagonal matrix it may (or) may not contains same diagonal elements. So it is False.Option(D) is not True in the given.Question 2.Matrix A-[aij]mxn is a square matrix ifA. m < nB. m > nC. m = 1D. m = nAnswer:Given that A is a matrix with m and n as their rows and columns respectively.We know that for a square matrix both m and n should be equalSo, m = n is the correct answer.Question 3.If then the values of x and y respectively areA. –2, 7B. C. D. 2, –7Answer:Given, = If the one matrix is equivalent to other matrix, then their elements should be equal.⇒ 3x + 7 = 1 & 5 = y-23x = -6 ; y = 7x = -2 ; y = 7∴ Option (A) is the answer.Question 4.If A = (1 -2 3) and then A + BA. (0 0 0)B. C. (-14)D. not definedAnswer:For matrix addition operation their no. of rows and no. of columns should be equal. Otherwise addition is not possible.In the given matrix A has 1 row and 3 columnsBut matrix B has 3 rows and 1 column.Since rows and columns are not equal it is not possible to add.So the answer is (d)Question 5.If a matrix is of order 2 × 3, then the number of elements in the matrix isA. 5B. 6C. 2D. 3Answer:Given that a matrix with order 2x3We know that the no. of elements in the matrix is equal to the product of no. of rows and no. of columnsi.e., No. of elements = No. of rows × No. of columns∴ No. of elements = 2 x 3= 6∴ There will be 6 elements in the given matrixSo, option (B) is the correct answer.Question 6.If then the value of x isA. 1B. 2C. D. 4Answer:Given,  Since both the matrix is equal to each other, the elements in it also be equal.By equalizing we will get x = 4So, option (D) is correct answer.Question 7.If A is of order 3 × 4 and B is of order 4 × 3, then the order of BA isA. 3 × 3B. 4 × 4C. 4 × 3D. not definedAnswer:Given matrix orders[A] with 3 x 4 and [B] with 4 x 3We have to find the order of [B].[A]For matrix multiplication the columns of 1st matrix and the rows of 2nd matrix should be equal.E.g. [A]3x2.[B]2x2The order of new matrix formed after multiplication of matrices will be 1st matrix row will be taken as new matrix rows. The no. of columns in 2nd matrix will be taken as new matrix columns.E.g. [A]3x2.[B]2x2 = [AB]3x2In the same way [B]4x3.[A]3x4 = [AB]4x4∴ option (B) is correct answerQuestion 8.If , then the order of A isA. 2 × 1B. 2 × 2C. 1 × 2D. 3 × 2Answer:Given,A x Let us consider as matrix B, it has an order of 2x2Let us consider the resultant matrix as C, it has an order of 1x2For matrix multiplication the columns of 1st matrix and the rows of 2nd matrix should be equal.So, matrix A has got same Columns as Rows of matrix BThe order of new matrix formed after multiplication of matrices will be 1st matrix row will be taken as new matrix rows. The no. of columns in 2nd matrix will be taken as new matrix columnsSo, matrix A has got same Rows as Rows of matrix CSo, Matrix A will consists of 1x2 order∴ option (C) is correct answerQuestion 9.If A and B are square matrices such that AB = I and BA = I, then B isA. Unit matrixB. Null matrixC. Multiplicative inverse matrix of AD. –AAnswer:It is based on a property about multiplication inverse. Only product of a matrix and its own inverse matrix then the resultant matrix will be identity matrix.AB = I and BA = ISo, B is the multiplicative inverse matrix of A∴ option (C) is correct answer.Question 10.If , then the values of x and y respectively, areA. 2, 0B. 0, 2C. 0, -2D. 1, 1Answer:Given, =  = By equating all the elements in the matrixWe will get 2 equationsx + 2y = 2 ⇒ 12x + y = 4 ⇒ 2By solving the both equations we will getx = 2; y = 0∴ option (A) is correct answerQuestion 11.If A = and A + B = O, then B isA. B. C. D. Answer:Given thatA + B = O ⇒ B = -A∴ B = B = ∴ option (B) is correct answerQuestion 12.If A = , then A2 isA. B. C. D. Answer:Given A = A2 = A×A = x = = = ∴ option (D) is correct answerQuestion 13.A is of order m x n and B is of order p x q, addition of A and B is possible only ifA. m = pB. n = qC. n = pD. m = p, n = qAnswer:Given matrix of A is m x n ⇒ [A]mxnMatrix of B is p x q ⇒ [B]pxqWe know that addition is possible is possible only the order is same for both the matricesSo, m = p, n = qSo, option (D) is trueQuestion 14.If , then the value of a isA. 8B. 4C. 2D. 11Answer: = By multiplying the matrices, we will get the value of ‘a’  = By equating the elements in the matrices2a-3 = 52a = 8a = 4So, option (B) is correct answerQuestion 15.If A = is such that A2 = I, thenA. 1 + α2 + βγ = 0B. 1 – α2 + βγ = 0C. 1 – α2 – βγ = 0D. 1 + α2 – βγ = 0Answer:Given A = A2 = II is the identity matrix  =  By comparing the elements in the matrix ⇒ ∴ Option (C) is correct answer.Question 16.If A = [aij]2x2 and aij = i + j, then A =A. B. C. D. Answer:Given A = [aij]2x2 and aij = i + jIt means matrix A with order 2x2 and the elements in is given by aij = i + ja11 = 1 + 1 = 2a12 = 1 + 2 = 3a21 = 2 + 1 = 3a22 = 2 + 2 = 4A = = ∴ Option (B) is correct answer.Question 17. , then the values of a, b, c and drespectively areA. -1, 0, 0, - 1B. 1, 0, 0, 1C. -1,0,1,0D. 1, 0, 0, 0Answer:Given By multiplying the matrices, we will get the values of a, b, c & d  By comparing the matrices on both sides-a = 1; -b = 0; c = 0; d = -1∴ Option (A) is correct answer.Question 18.If , then the matrix B =A. B. C. D. Answer:GivenA + B = ; A = B = B = = = ∴ Option (C) is correct answer.Question 19.If , then the value of x isA. 7B. -7C. D. 0Answer:Given    By equating the elements13 – x = 20x = -7∴ Option (B) is correct answer.Question 20.Which one of the following is true for any two square matrices A and B of same order?.A. (AB)T = ATBTB. (ATB)T = ATBTC. (AB)T = BAD. (AB)T = BTATAnswer:This is Reversal law for transpose of matrices∴ (AB)T = BTAT∴ Option (D) is correct answer.

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