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Mathematics for Data Science II · Quiz 1 · 30 Jan 2022 · January 2022 term · Set QPB1

Question 4: Consider the following sets with the given operations def…

Question 4

+6 marksOne or more correct options

Consider the following sets with the given operations defined as follows:

  • W1={(x,y,z)∣x,y,z∈R,x+y+z=1}W_1 = \{(x, y, z) \mid x, y, z \in \mathbb{R}, x + y + z = 1\}

    Addition: (x1,y1,z1)+(x2,y2,z2)=(x1+x2,y1+y2,z1+z2); (x1,y1,z1),(x2,y2,z2)∈W1(x_1, y_1, z_1) + (x_2, y_2, z_2) = (x_1 + x_2, y_1 + y_2, z_1 + z_2); \ (x_1, y_1, z_1), (x_2, y_2, z_2) \in W_1

    Scalar multiplication: c(x,y,z)=(cx,cy,cz); (x,y,z)∈W1, c∈Rc(x, y, z) = (cx, cy, cz); \ (x, y, z) \in W_1, \ c \in \mathbb{R}

  • W2={(x,y,z)∣x,y,z∈R,x=y−z}W_2 = \{(x, y, z) \mid x, y, z \in \mathbb{R}, x = y - z\}

    Addition: (x1,y1,z1)+(x2,y2,z2)=(x1+x2,y1+y2,z1+z2); (x1,y1,z1),(x2,y2,z2)∈W2(x_1, y_1, z_1) + (x_2, y_2, z_2) = (x_1 + x_2, y_1 + y_2, z_1 + z_2); \ (x_1, y_1, z_1), (x_2, y_2, z_2) \in W_2

    Scalar multiplication: c(x,y,z)=(cx,cy,cz); (x,y,z)∈W2, c∈Rc(x, y, z) = (cx, cy, cz); \ (x, y, z) \in W_2, \ c \in \mathbb{R}

Based on the above data, answer the given subquestions.

Which of the following options are true for W1?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • C
  • D
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Question 4 of 12 in the IIT Madras BS Mathematics for Data Science II (Maths 2) Quiz 1 paper sat on 30 Jan 2022, in the January 2022 term (IIT M FOUNDATION QUIZ EXAM QPB2 30 Jan 2022). It carries 6 marks.

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