Mathematics | Class 11| Question Bank - Matrices and Determinants

 Mathematics Question Bank - Matrices and Determinants

Question 1.
If A = [13−24] . Find 2A and 3A
Answer:

Question 2.

If A = [16−3254] find 5A’.
Answer:

Question 3.
If A = [1−1234−2] and B = [31−45−1−2] .Find A+ B and A – B
Answer:

Question 4.

If  [x+y23−y+x]+[2431]=[0660] . Find x and y.
Answer:
Question 5.

If  [x221−1]+[2x−122]=[−1131] Find x.
Answer:

⇒ x2 + 2x = -1
x2 + 2x + 1 = 0
(x + 1)2 = 0 ⇒ x + 1 = 0
⇒ x = -1

Question 6.
If A = ⎡⎣⎢400040004⎤⎦⎥ . Find A – A’
Answer:

Question 7.
If A = [2x−x−7] . Find A + A’.
Answer:
Question 8.

If A = [132−1] B = [2−35−1] C = [14−1−3] Find 2A – 3B – C
Answer:

Question 9.
Find the matrix A. if 2A + B = [210−3] , where u = [13−10]
Answer:

Question 10.
If A = [34−15] , Find X such that A – 2x = [124−3] .
Answer:

Question 11.
If A + B + C = 0 where A = ⎡⎣⎢321−204⎤⎦⎥ , B = ⎡⎣⎢2−4−3−123⎤⎦⎥ . Find C
Answer:

Question 12.
If A = B = [3−314] verify (A – B)’ = A’ – B’
Answer:

Part – B

2nd PUC Basic Maths Matrices and Determinants Ex 1.1 Two Marks Questions and Answers

Question 1.
If A = ⎡⎣⎢402−13−3⎤⎦⎥ . Find (i) 5A2(ii)−2A3 .
Answer:

Question 2.
If A = [1−130−12] and B = [41−132−2] . Find (i) 2A + 3B (ii) A – 3B (iii) A + 12B.
Answer:

Question 3.
If A = [3124] B = [1−2−13] and C = [−324−1] . Find 34A – 2B – 4C
Answer:

Question 4.
If A = [1−4−3−1] and B = [3−541] and 0 is a null matrix of order 2 × 2. Find the matrix C such that
(i) 2C = A + B
(ii) A + C = 0
(iii) B + 5c = A
(iv) 3A + 5B + 2C = 0
Answer:

Question 5.

Answer:

Question 6.
Find x and y given that [−92]−[5−1]=[xy]
Answer:

Question 7.
If A = [351643x+1] and B = ⎡⎣⎢314563⎤⎦⎥ .
Find x given that A = B’
Answer:

Question 8.
Solve for x and y x[21]+y[35]+[46]=[1217] .
Answer:

⇒ 2x + 3y + 4 = 12
x + 5y + 6 = 7
⇒ 2x + 3y = 8 …. (1) solving these equations
x + 5y = 11 ….. (2) × 2

and x = 11 – 5y = 11 – 10 = 1
∴ x = 1, y = 2

Question 9.
Find x and y given that [x+y−13x−y]=[4−138]
Answer:

Question 10.
If [2735]+[2y−1x−25]=[47110] Find x and y-1
Answer:

⇒x + 1 = 1 ⇒ x = 0
y + 6 = 7 ⇒ y = 1
∴ x = 0, y = 1

Part – C

2nd PUC Basic Maths Matrices and Determinants Ex 1.1 Three Marks Questions and Answers

Question 1.
Find A and B if
(a) 2A + B = [10−11] and A – 3B = [0110] .
(b) 2A + B = [213410] , 3A + B = [426315]
(c) 2A – 3B = [2−12−41] , A + 5B = [133247]
(d) 2A + B = [3−2−15] and A – 2B = [4−125] .
Answer:

Question 2.
If A = ⎡⎣⎢3278−6413−5⎤⎦⎥ , B = ⎡⎣⎢461023232⎤⎦⎥ . verify 3(A + B) = 3A + 3B.
Answer:

Question 3.
Find x, y, a, b if = [3x+4ya+b22a−bx−2y−1]=[252−54−1]
Answer:

Question 4.
Find x if [x3313]+[−2x2134]=[−x447]
Answer:

⇒ x3 – 2x2 = x; x3 – 2x2 + x = 0 ; x(x2 – 2x + 1) = 0
x = 0 or (x – 1)2 = 0 ⇒ x = 0 or x = 1

Question 5.
If A = [2−2−1130] , B = [−15014−3] C = [46−121−1] . Find the matrix X such that 2A – 3B – x = C
Answer:

Question 6.
Find a,b,c given that 4⎡⎣⎢a4725−83−69⎤⎦⎥−5⎡⎣⎢3b926−81−47⎤⎦⎥=⎡⎣⎢136−17−2−52c7−41⎤⎦⎥
Answer:

Credit: KSEEB Solutions