3. Let A: 3 3 -1 1 -2 2 V₁ = 1 V₂ V3 = V₁ and use the facts Av₁ =V₁ A√₂ = √₂ AV3 = V3 V4 € Nul(A) to answer the following questions. You di houe

Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

A:

Q: 7. Show that

A:

Q: 3. Let A = {1, 2, 3}. What is |A|?

A: If A = {x,y,z}  |A| = sqrt x^2 + y^2 + z^2

Q: 11 |72.6

A:

Q: 8. Let a, b and c be any positive real numbers. Prove that b² + c² a²+b² 2c a² + c² + 2b 2a > a+b+c.

A:

Q: let a,b,c,d,e and f be different positive integers so that a² - b² = c² - d² = e² - f² = 63. Value a…

A: Given:- a,b,c,d,e and f are different positive integers.  also a2-b2=c2-d2=e2-f2=63. To find :- the…

Q: Find L¹ S 5²-48-7)

A:

Q: а) За — 5 <7х + 7 -6 –5 –4–3 -2 – 1 1 2 4 5 3

A:

Q: 4. 1 + 2 + 2² + 2³ + ... + 2^-¹ = 2^-1 +2²+2³+...+2n-1

A:

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: 3. Determine all the units of Z40 and of Z11.

A:

Q: 2. Find 14 --3-6 -8 7) 4

A: To find the product matrices.

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              =&gt; k(15 - 13) = 2k for any integer k              =&gt; 15 k -…

Q: 1+x dr 1+ x?

A:

Q: -5² + 3(¯5)² 50 O -50 O 49 O -49

A:

Q: с. In(х + 2) +Inx —D In(x + 12)

A:

Q: hy?

A: The expression given as, 2∈2. In the set-roaster notation, all the elements of a set exist between…