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Federal (FBISE) · Chapter test · Free

10th Class Mathematics Chapter 3 Test03. Matrices and Determinants

30 marks · 40 minutes · 21 questions. Covers: 03. Matrices and Determinants.

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10th Class Mathematics Chapter 3 Test

10th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. If A and B are two matrices, conformable for the product AB then (AB)t=(AB)^t =
    1. AtBtA^tB^t
    2. (BA)t(BA)^t
    3. BtAtB^tA^t
    4. AB
  2. Matrix equation for y + x = 144 + y and x + 2y = x + 13 is
    1. [1112]×[xy]=[14413]\begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix} \times \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 144 \\ 13 \end{bmatrix}
    2. [1012]×[xy]=[14413]\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix} \times \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 144 \\ 13 \end{bmatrix}
    3. d) [1012]×[xy]=[1413]\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix} \times \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 14 \\ 13 \end{bmatrix}
    4. [1002]×[yx]=[14413]\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix} \times \begin{bmatrix} y \\ x \end{bmatrix} = \begin{bmatrix} 144 \\ 13 \end{bmatrix}
  3. Multiplicative inverse of a null matrix of order 2, is
    1. [0000] \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}
    2. [00] \begin{bmatrix} 0 & 0 \end{bmatrix}
    3. [00] \begin{bmatrix} 0 \\ 0 \end{bmatrix}
    4. Impossible
  4. If I3=[y0x0z0x01] I_3 = \begin{bmatrix} y & 0 & x \\ 0 & z & 0 \\ x & 0 & 1 \end{bmatrix} then
    1. y = x = 1
    2. x = z = 0
    3. x = z = 1
    4. y = z = 1 , x = 0
  5. [12][3]=\begin{bmatrix} 1 & 2 \end{bmatrix} \begin{bmatrix} 3 \end{bmatrix} =
    1. [36]\begin{bmatrix} 3 &6 \end{bmatrix}
    2. [36] \begin{bmatrix} 3 \\ 6 \end{bmatrix}
    3. [5]
    4. Impossible
  6. The matrix of coefficients for x - y = 3, is
    1. [3]
    2. [1−1] \begin{bmatrix} 1 \\ -1 \end{bmatrix}
    3. [1−1]\begin{bmatrix} 1 & -1 \end{bmatrix}
    4. [xy] \begin{bmatrix} x \\ y \end{bmatrix}
  7. If adj A=[5623]A = \begin{bmatrix} 5 & 6 \\ 2 & 3 \end{bmatrix} then | A | =
    1. | adj A |
    2. ∣At∣| A^t |
    3. | - A |
    4. All of these
  8. [12]+[00]\begin{bmatrix} \frac{1}{2} \end{bmatrix} + \begin{bmatrix} 0 \\ 0 \end{bmatrix}=
    1. [12]\begin{bmatrix} \frac{1}{2} \end{bmatrix}
    2. [12] \begin{bmatrix} 1 \\ 2\end{bmatrix}
    3. [1020] \begin{bmatrix} 1 & 0 \\ 2 & 0 \end{bmatrix}
    4. Impossible
  9. [1525]×[32]=\begin{bmatrix} 15 \\ 25 \end{bmatrix} \times \begin{bmatrix} 3 & 2 \end{bmatrix} =
    1. [95]
    2. [4550]\begin{bmatrix} 45 \\50 \end{bmatrix}
    3. [4550] \begin{bmatrix} 45 & 50 \end{bmatrix}
    4. [45307550] \begin{bmatrix} 45 & 30 \\ 75 & 50 \end{bmatrix}
  10. A is a symmetric matrix if
    1. At≠AA^t ≠ A
    2. (At)t≠−A(A^t)^t ≠ -A
    3. (At)t=−A(A^t)^t = -A
    4. (At)t=At(A^t)^t = A^t

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Verify A(B + C) = AB + AC A=[52],B=[64] and C=[12]. A = \begin{bmatrix} 5 & 2 \end{bmatrix}, B = \begin{bmatrix} 6 \\ 4 \end{bmatrix} \text{ and } C = \begin{bmatrix} 1 \\ 2 \end{bmatrix}.
  2. If P=[5329] and Q=[7239]. P = \begin{bmatrix} 5 & 3 \\ 2 & 9 \end{bmatrix} \text{ and } Q = \begin{bmatrix} 7 & 2 \\ 3 & 9 \end{bmatrix}. , then verify the commutative property of matrix addition.
  3. If C=[2060],D=[26],E=[2266] C = \begin{bmatrix} 2 & 0 \\ 6 & 0 \end{bmatrix}, D = \begin{bmatrix} 2 \\ 6 \end{bmatrix}, E = \begin{bmatrix} 2 & 2 \\ 6 & 6 \end{bmatrix} . Then check whether C + D = E
  4. Write the most appropriate type of the matric. [15×39×5]\left[ \frac{15 \times 3}{9 \times 5} \right]
  5. Find x, y , z from the following, if possible. Mention the reason if not possible.xxi) Find x, y, z from the following, if possible. Mention the reason. [51015x]+[5y155]=[z15307] \begin{bmatrix} 5 & 10 \\ 15 & x \end{bmatrix} + \begin{bmatrix} 5 & y \\ 15 & 5 \end{bmatrix} = \begin{bmatrix} z & 15 \\ 30 & 7 \end{bmatrix}
  6. If A=[5326] and B=[7249]. A = \begin{bmatrix} 5 & 3 \\ 2 & 6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 7 & 2 \\ 4 & 9 \end{bmatrix}. then find AB and BA. Also check whether AB = BA or not. What is concluded from the result?
  7. If A=[1023],B=[210−3] A= \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix}, B=\begin{bmatrix} 2 & 1 \\ 0 & -3 \end{bmatrix}then. Find AB and BA , check whether AB = BA or not?
  8. If B=[210−3] B=\begin{bmatrix} 2 & 1 \\ 0 & -3 \end{bmatrix}then find B²

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. The daily sum of labour and the material costs of Haani's and Massab's Home Industries are Rs. 20,000 and Rs. 40,000 respectively. If labour and the material rate, for both the Home Industries is same but Hanni's Home Industry has 6 workers who make 80 items and Massab's Home Industry has 12 workers who make 160 items, find the labour and the material cost.
  2. If A=[1023],B=[210−3], A = \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & 1 \\ 0 & -3 \end{bmatrix}, then Verify that (AB)t=BtAtandA(AB)^t = B^tA^t and A
  3. Verify Associative property of matrix multiplication for:X=[5326],Y=[1−754],Z=[64] X = \begin{bmatrix} 5 & 3 \\ 2 & 6 \end{bmatrix}, Y = \begin{bmatrix} 1 & -7 \\ 5 & 4 \end{bmatrix}, Z = \begin{bmatrix} 6 \\ 4 \end{bmatrix}