möbius

2023-24 CIVE299- Engineering Mathematics II CIVE299 Assignment 2

CIVE299 Assignment 2

- Question 8

2 points

How Did I Do?

Consider a 3 x 3 upper triangular matrix B with main diagonal elements 3, 8 and 8.

Suppose that a matrix A was obtained from matrix B by making the following row operations on B:

.multiplying row 2 of B by 6, and

adding 8 times row 3 to row 1.

What is the determinant of A?

det (A) =

absin (a)

8

𐐀х

f

∞

a

Ω

Remaining Time: Unlimited/nQuestion 7

3 points

How Did I Do?

g

CIVE299: Assignment 2 (15%)

Format:

If your answer is a vector, enter it as a column vector using the matrix tool button.

In this question you need to find four numbers. Enter these values, in order, separated by commas (e.g. 1,2,3,4).

The vectors

--0-0-0-0-

Olinearly independent.

Olinearly dependent.

a sin (a)

old

and

If the vectors are linearly dependent, demonstrate this by finding constants a, b, c and d, not all 0, such that

-f

1

8

If they are independent, so no such constants exist, take each of the four values to be 0 (that is, enter 0,0,0,0).

a, b, c, d =

m University of Liverpool - CIVE299 Assignment

are

a S2

aw+bx+cy + dz = 0.

III ?/nmöbius

2023-24 CIVE299- Engineering Mathematics II / CIVE299 Assignment 2

CIVE299 Assignment 2

- Question 6

CIVE299: Assignment 2 (15 %)

2 points

How Did I Do?

A3 x 3 matrix A has determinant equal to -18.

A new matrix B is created from A by swapping row 2 and row 1.

What is the determinant of B?

det (B) =

asin (a)

8

ar

f

⠀

∞

α Ω S2

m University of Liverpool - CIVE299 Assignment 2

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CIVE299 Assignment 2

Question 5

3 points

How Did I Do?

A student is trying to solve

where A =

ab

-8

-8

1 5

-1

8 3

1

To find the value of z, the student needs to calculate the determinants of two matrices. One of those matrices is A. What is the other matrix?

sin (a)

Ә

da

6, using Cramer's rule.

***

α

A

52

Ω

10

Remaining Time: Unlimited/nCIVE299: Assignment 2 (15%)

b.

C.

Now, and for the remainder of this question, instead set d=-6, so

7

2 11

-649

A 0 -6 1

5

0

8

Calculate the matrix of cofactors for the matrix A.

matrix of cofactors===

ab sin (a)

dr

absin (a)

⠀⠀⠀ ∞o

8

dz

a

***

Ω

Show/hide

00 a Ω

m University of Liverpool - CIVE299 Assignment 2

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Use the information above to find the inverse matrix A-1, employing the method of cofactors. (This part still uses that d=-6.)

A-1-

m

11

G

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2023-24 CIVE299-Engineering Mathematics II CIVE299 Assignment 2

CIVE299 Assignment 2

Question 4

CIVE299: Assignment 2 (15%)

12 points

How Did I Do?

Format:

Find d such that det A= 0, where

(7 2 11)

A=0 d 1

508

Remember: Möbius does not check your method, and matrix computations are fiddly. Make sure to check your answers carefully before

submitting.

If your answer is a vector, enter it as a column vector using the vector/matrix palette tool.

d=

ab

sin (a)

8

Oz

⠀⠀

∞

a

52

m University of Liverpool - CIVE299 Assignment 2

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P

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Next/nReminder: check the formatting instructions above.

Finally, in the case where there is exactly one solution, find the formulas for x and y in terms of a and b.

ab

y =

ab

sin (a)

sin (a)

8

dr

old

8

a

α

Ω

52

E

III

G

团/ne. In the case(s) where the choices of a and b mean there are infinitely many solutions, the variables and y are related by an

equation. Rearrange the equation to find the formula for y in terms of a

y =

a

sin (a)

Ə

Əx

8

a Ω/n3.

-4

-3

y

-2 -1

-4-

4-

/0

1

2

X

3

4

Submit Assignment

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-2

4

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