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Worksheet on Matrix

In Worksheet on matrix the questions are based on finding unknown elements and matrices from matrix equation.

1. Let A = [1223], B = [2132] and C =  [1331]

(i) Find the matrix C(B – A).

(ii) Find A(B + C).

(iii) Prove that A(B + C) = AB + AC.

2. If A =  [3210], B =  [1301] then verify the truth of the following.

(i) (A + B)2 = A2 + B2 + 2AB

(ii) (A + B)(A – B) = A2 – B2


3. If X =  [4112], show that 6X – X2 = 9I, where I is the unit matrix.

4. (i) Show that X = [1221] satisfies the relation X2 – 2X – 3I = O, where I is the unit matrix of order 2 × 2 and O is the null matrix of order 2 × 2.

(ii) Let A = [1021], B = [2310]. Find A2 + AB + B2.


5. Find the matrix X from the matrix equation [2150] – 3X = [7426].

6. (i) If A = [1x01] and [345y] such that A + 2B = 5[75021] then find x and y.

(ii) If 2[345x] + [1y01] = [7x105], find x and y.


7. If [4xy][21] = [846384], find x and y.

8. If [4567][xy] = [12], find x and y.

9. If [1233][x00y] = [x090], find x and y.

10. If [3205][x2] = [5y], find x and y.

11. If [2340][x1y1] = [4z34], then find x, y and z.

Worksheet on Matrix

12. Let A = [21201] and B = [4x01]. If A2 = B, find x.

13. Let A = [1313] and B = [3ab2]. If AB = O, where O is the null matrix, find a and b.

14. Find x and y if [x3xy4y][21] = [512].

15. Let A = [2134]. Find the matrix B such that A2 = 2A + 3B.

16. Let A = [1324], B = [12] and C is a matrix such that AC = B then find the matrix C.

17. Let A = [2134]. Find the matrix B such that AB = I, where I is the unit matrix of the order 2 × 2.

18. Given A = [2120], B = [3240] and C = [1002]. Find the matrix X such that A + X = 2B + C.

19. If [1423] + 2M = 3[3203], find the matrix M.

20. (i) Show that X = [1221] satisfies the relation X2 – 2X – 3I = O, where I is the unit matrix of order 2 × 2 and O is the null matrix of order 2 × 2.

(ii) Let A = [1021], B = [2310]. Find A2 + AB + B2.

Answers:

 

1. (i) [4444]

(ii) [15102417]


2. (i) False

(ii) False


4. (ii) [4954]

5. [3112]

6. (i) x = -8, y = 2

(ii) x = 2, y = -8


7. x = 3, y = -4

8. x = 358, y = 729

9. x = 3, y = 0

10. x = 3, y = -10

11. x = 34, y = 56, z = 5

12. x = 36

13. a = -6, b = -1

14. x = 1, y = 2

15. [1434113]

16. [1525]

17. [45153525]

18. [7562]

19. [4116].

20. (ii) [4954].





10th Grade Math

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