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Solve the system of linear equations using matrix inverse method.

x-y+z=1

2y-z=1

2x+3y=1

The following were obtained by applying Kirchoff’s laws to an electric circuit

2IA +IB −IC = −8

−IA +IB +IC = 3

−2IA +4IC = 18

Use the matrix method (together with elementary row transformations) to solve the following:

2x −y +3z = 2

x +2y −z = 4

−4x +5y +z = 10

Determine the inverse of A, and show that A

−1A = I.

A =

(2 1 0

2 −1 1

3 −2 4)

Instructions

1. Find A-B using the following matrices:

5

6 1

2

9

3

A=-3

5

8

B=|

81

4

3

3

4

67

-5

-1

2. Find AB using the following matrices:

A=

1 2

3

B=

7

9

8

10

4 5 6

11

12

QUESTION 1. [34 MARKS] 1.1 Determine whether each of the following mappings T is linear, or not. Justify your answer.

(a) T: R2 - R3, where T(z, y) = (3y, 2x, —y).

(b) T: P1 - R2, where T[p(x)] = [p(0), p(1)].

(c) T: R3 - R2, where T(z, y,z) = (x+1,y+2).

Solve for x in the given matrix equalities

det (x −3 4

3 −5 x

1 2 −1)= 45

Determine the value of the unknown in the given matrix equalities

(2 −1 x

4 7 0)

(x 3

−2 5

1 −4)

=

(4 −2

1 5 )

. Determine the value of the unknown in the given matrix equalities

(i)

(5 −2

−4 3 )+

(x y

w z)

=

(2 −1

3 6 )

Let 𝐴=   1 1 1 3

2 0 4 6

1 1 3 7

a. What size is A?

b. What is the third column of A?

c. What is the second row of A?

d. What is the element of A in the (3,2)th position?

e. What is A’?

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