2023-24 CIVE299- Engineering Mathematics II CIVE299 Assignment 2

CIVE299 Assignment 2

Question 3

16 points

How Did I Do?

Format:

. If you have more than one answer to a question, enter your answers separated by a comma.

• If no solution exists, enter the single character "n" (without the quote marks).

. Give your answers in exact form (i.e. do not use decimal approximations).

• Use to explicitly indicate multiplication between variables and other variables, between variables and brackets, or between sets of

brackets (e.g. x*y rather than xy; 2*(x+y) rather than 2(x+y)).

Here is a system of two linear equations with two unknown constants a and b.

a.y+6-z=4

6 a z+4 y 6-b

b. Match the graphs to the cases:

-- Infinitely many solutions

a. Write down the matrix of coefficients and the augmented matrix, and put both into echelon form.

Which statement is true about the rank of the two matrices?

The rank of both matrices is always 2, independent of the values of a and b.

O The rank of both matrices is always 1, independent of the values of a and b.

The rank of one matrix depends on the values of a and/or b, but the rank of the other matrix does not.

O The ranks of both matrices depend on the values of a and/or b.

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