Chapter 3 MATRICES EXERCISE 3.2 Question

NCERT Solutions for Class 12 Maths – Chapter 3 – MATRICES EXERCISE 3.2

Question 1. Let

    A = [2   4]    B = [1   3]    C = [-2   5]
        [3   2]        [-2  5]        [ 3   4]
    

Find each of the following:
(i) A + B
(ii) A – B
(iii) 3A – C
(iv) AB
(v) BA

Question 2. Compute the following:

(i)

    [a   b]    [a   b]    
    [-b  a] +  [b   a] 
    

(ii)

    [a² + b²   b² + c²]     [2ab        2bc]    
    [a² + c²   a² + b²]  +  [-2ac      -2ab]  
    

(iii)

    [-1  4  -6]   [12  7   6]   
    [ 8  5  16] + [ 8  0   5] 
    [ 2  8   5]   [ 3  2   4]   
    

(iv)

    [cos²(x)   sin²(x)]   [sin²(x)   cos²(x)]   
    [sin²(x)   cos²(x)] + [cos²(x)   sin²(x)] 
    

Question 3. Compute the indicated products.

(i)

    [a  b]    [a  -b]    
    [-b a] *  [b   a]  
    

(ii)

    [1]       
    [2]  * [2  3  4]           
    [3]           
    

(iii)

    [1   -2]  *  [1   2   3]  
    [2    3]     [2   3   1]    
    

(iv)

    [2  3  4]    [1  -3  5]   
    [3  4  5]  * [0   2  4]  
    [4  5  6]    [3   0  5]  
    

(v)

    [2   1]    [1   0  1]    
    [3   2]  * [-1  2  1]  
    [-1  1]                
    

(vi)

    [3   -1    3]    [2  -3]   
    [-1   0    2]  * [1   0] 
                     [3   1]              
    

Question 4 if

       [1   2   -3]       [3   -1    2]        [4   1   -1]
  A =  [5   0    2]  B =  [4    2    5]   C =  [0   3    2]
       [1  -1    1]       [2    0    3]        [1  -2    3]
    

, then compute (A+B) and (B – C). Also, verify that A + (B – C) = (A + B) – C

Question 5 If

            [2/3   1     5/3]      [2/5   3/5   1  ]
    A =     [1/3   2/3   4/3] B =  [1/5   2/5   4/5]
            [7/3   2     2/3]      [7/5   6/5   2/5] 
       
    

then compute 3A – 5B.

Question 6. Simplify

    cosθ * [cosθ    sinθ]    + sinθ *  [sinθ   -cosθ]
           [-sinθ   cosθ]              [cosθ   sinθ]
    

Question 7. Find X and Y, if

(i)

    X + Y = [7  0]
            [2  5]

    X - Y = [3  0]
            [0  3]
    

(ii)

    2X + 3Y = [2   3]
              [4   0]

    3X + 2Y = [2   -2]
              [-1   5]
    

NCERT Solutions for Class 12 Maths – Chapter 3 – MATRICES EXERCISE 3.2 Question 1 to 7

Question 8. Find X, if

    Y = [3  2]    and  2X + Y = [1   0]
        [1  4]                  [-3  2]

Question 9. Find x and y, if

    2 * [1  3] + [y   0]  = [5  6]
        [6  x]   [1   2]    [1  8]

Question 10. Solve the equation for x, y, z and t, if

    2 * [x  z] + 3 * [1   -1]  =3 *  [3  5]
        [y  t]       [0    2]        [4  6]

Question 11. If

    x * [2] + y * [-1]  =     [10]
        [3]       [ 1]        [ 5]

, find the values of x and y.

Question 12. Given

    3 * [x  y]   =   [x    6]  +    [4     x + y]
        [z  w]       [-1  2w]       [z + w     3]
        
 find the values of x, y, z and w.

Question 13.If

        [cosx   -sinx   0]
F (x) = [sinx   cosx    0]
        [ 0     0       1]
        show that F(x) F(y) = F(x + y).

Question 14. Show that

    [5  -1][2  1]   ≠  [2  1][5  -1]
    [6   7][3  4]      [3  4][6   7]