10th Class Mathematics Unit 3 Matrices and Determinants Numericals with Solutions

3.1.1.Write the number of rows and number of columns in each matrix. (i) A = [[0,0],[0,0]] (ii) B = [[3],[4],[7]] (iii) C = [8, -10, 11] (iv) D = [[3,2,1],[1,0,3],[4,5,6]] (v) E = [[5,9,-2],[-3,4,5]] (vi) 6x+6 / (20-x) = 1/x, x ≠ 0, 20 — write in matrix form.

Given

Matrices A=begin{bmatrix}0&00&0end{bmatrix}, B=begin{bmatrix}347end{bmatrix}, C=begin{bmatrix}8&-10&11end{bmatrix}, D=begin{bmatrix}3&2&11&0&34&5&6end{bmatrix}, E=begin{bmatrix}5&9&-2-3&4&5end{bmatrix}

Result

(i)-(v) A:2 × 2, B:3 × 1, C:1 × 3, D:3 × 3, E:2 × 3

Working

(vi) Cross multiply (6x+6)x = 1(20-x)

6x²+6x = 20-x

Result

Standard form / matrix form 6x²+7x-20=0 ⇒ begin{bmatrix}6&7&-20end{bmatrix}, Rows=1, Columns=3

3.1.2.Write the order of each matrix. (i) A=[[1],[0]] (ii) B=[3,4] (iii) C=[[3,5],[5,6]] (iv) D=[[0,3,4],[5,0,9]] (v) E=[[0,1],[3,4],[5,6]] (vi) F=[5]

Given

Matrices A,B,C,D,E,F

Result

Orders A:2 × 1, B:1 × 2, C:2 × 2, D:2 × 3, E:3 × 2, F:1 × 1

3.1.3.Which of the following matrices are equal? A=[[0,3],[4,1]], B=[[9],[-7]], C=[[2×3,2-1],[2×2,4-2],[4+4,3+0]], D=[[5+4],[-8+1]], E=[[6,1],[4,2],[8,3]], F=[[3-3,3],[3+1,1]]

3.1.4.If [[a+2, c-3],[b-1, d+4]] = [[5,8],[6,4]], then find the values of a, b, c and d.

Formula

Equate corresponding elements a+2=5, c-3=8, b-1=6, d+4=4

a=3, c=11, b=7, d=0

Result

Answer a=3, b=7, c=11, d=0

3.1.5.If [[2x+1,4],[7,5]] = [[9,4],[7,y]], then find the values of x and y.

Formula

Equate corresponding elements 2x+1=9,quad 5=y

2x=8 ⇒ x=4

Result

Answer x=4, y=5

3.1.6.If [[a+b,2d-1],[3b+2,4]] = [[10,5],[11,c]], then find the values of a, b, c and d.

Formula

Equate corresponding elements a+b=10, 2d-1=5, 3b+2=11, 4=c

d=3, b=3, c=4

From a+b=10 a+3=10 ⇒ a=7

Result

Answer a=7, b=3, c=4, d=3

3.1.7.If [[p+q,5],[11,p-2q]] = [[6,5],[11,0]], then find the values of p and q.

Formula

Equate corresponding elements p+q=6,quad p-2q=0

From p-2q=0 p=2q

Working

Substitute in p+q=6 2q+q=6 ⇒ 3q=6 ⇒ q=2

Result

Answer p=2(2)=4, q=2

Unit 3: Matrices and Determinants — Exercise 3 1