Homework Answers

Solve for the determinant in the equation below(10marks)

1.7.1

"\\begin{matrix}\n 4 & -3 & 2 \\\\\n 1 & 2 &-2 \\\\\n 2 & -1 & -4\\\\\n\n\\end{matrix}"

1.7.2.

"\\begin{matrix}\n 2 & -2 & 1 \\\\\n 2 & 2 & 1\\\\\n 4 & 1 & 3 \\\\\n\\end{matrix}"

A fair coin tossed 400 times.If X is the number of heads obtained, find the expected value and variance of X

1.5 Solve the equation below using Inverse method (10 marks)

"\\begin{bmatrix}\n 1 & 3 & 0 \\\\\n 0 & 0.5 & 1\\\\\n0.05 & 0 & 1\\\\\n\n \\end{bmatrix}" "\\begin{bmatrix}\n x \\\\\n y\\\\\nz\\\\\n\\end{bmatrix}" ="\\begin{bmatrix}\n 4 \\\\\n 1\\\\\n3\\\\\n\\end{bmatrix}"

Using a Truth table, determine the value of the compound proposition(10marks)

((𝑝 ∨ 𝑞) ∧ (￢𝑝 ∨ 𝑟)) → (𝑞 ∨ 𝑟).

How many positive integers less than 1000 have at least one decimal digit equal to 9?

Solve for the determinant in the equation below. (10)

1.7.1.

4 −3 2

1 2 −2

2 −1 −4

1.7.2

2 −2 1

2 2 1

4 1 3