Quiz 1

MATH1014: Introduction to Linear Algebra

线性代数导论代写 2.Find the normalisation of w = 7i − 25j − 24k. 3.Find parametric equations for the line in R3 through A = (7, −5, 3) and B = (3, −11, 8). 

2.

Find the normalisation of w = 7i − 25j − 24k.

3.

Find parametric equations for the line in R³through A = (7, −5, 3) and B = (3, −11, 8).

4.

Write down a Cartesian equation for the plane in R³orthogonal to n = −2i + 10j + 6k and containing the point P = (1, 5, −6).

5.  线性代数导论代写

Determine a Cartesian equation for the plane in R³containing the points X = (2, 2, −6), Y = (7, 9, 3), and Z = (−1, −2, −5).

6.

Let ` be the line through A = (8, 4, −11) and B = (−2, 6, −5). Find a value c ∈ R such that ` passes through the point C = (38, −2, c).

7.

Give a direction vector for the line of intersection of the planes 3x + 4y − 9z = 10 and −9x + y − 10z = 7.

8.

Calculate 4¹²− 3¹⁴in Z₁₀.

9.  线性代数导论代写

Calculate 11²⁰¹⁸in Z₁₉.

10.

Solve the equation x³+ 3x²+ 3 = 0 in Z₅.

11.

What is the inverse of 5 in Z₂₂?

12.

Write down the parity check code vector for the binary vector [1, 0, 0, 1, 1, 0, 1, 0].