Linear Algebra Answers

2X1+2X3-x3+x5=6,-X1-x2+2X3-3X4+X5=0,X3+X4+X5=0,X3+X5+X5=0 SOLVE IT BY USING GUASS JORDON METHOD

List of row vectors and column vectors of the matrix.

[2 -1 0 1

3 5 7 -1

1 4 2 7]

Find the solution set of x1+2x2-3x3+x4=0

3X1-X2+5X3-X4=0

2X1+X2+X4=0

Find the solution x1+2x2-3x3+x4=0

3x1-x2+5x-3x4=0

2x1+x2+x4=0

Find an expression for a square matrix A satisfying A squared

= In, where In is the n × n identity matrix. Give 3

examples for the case n = 3. 

suppose that A,B,C and D are matrices with the following sizes: A(5 x 2) B(4 x 2) C(4 x 5) D(4 x 5)

determine in each of the following case whether a product is defined. if it is so then give the size of the resulting matrix.

i) BD

ii) AC - B

iii) DC + A

A company makes products A and B. Each unit of product A requires 1 unit of resource 1 and 5 units

of resource 2. Each unit of product B requires 5 units of resource 1 and 4 units of resource 2. If there

are 40 units of resource 1 and 140 units of resource 2 available, how many units of each product should

be produced if all the resources are to be used?

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

Check whether 𝑇 ∶ ℝ2 → ℝ2

, defined by 𝑇 (𝑥, 𝑦) = (−𝑦, 𝑥) is a linear transformation.

2. State at least 2 application of cryptography in engineering.