7 = (–9,6, –1) ≤ R³

Q: Q4. Use Pascal's triangle to expand (3 + x)°.

A:

Q: Consider 2x° – 3y? = 8 -

A: SolutionStep I :  2x3 - 3y2 = 8Now, 2x3-3y2=8⇒2x3-8 = 3y2ddx2x3-8 = ddx3y26x2 =…

Q: Show that Sn is solvable when n ≤ 4.

A: We see that S1  is the trivial group {e} and it is solvable.   We see that , |S2| = 2 so it is…

Q: . Let a, b € Z so that 4a + 5b is a multiple of 13. Prove that 13 divides 9a + 8b.

A: We have to show that 13 divides 9a+8b To prove this we using 4a+5b divisible by 13

Q: Ex. Show that [b, c) ~ [a, o), where a, b, c ER and b< c. [H7-9]

A:

Q: need to find the formula

A:

Q: R² = gen gen

A: see below the reason

Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: To show that the group &lt;a, b | a^5 = b^2 = e, ba = a^2b&gt; is isomorphic to Z2, we need to…

Q: Show that is isomorphic to Z2.

A:

Q: Suppose the multiplication cx is defined to produce (cx1, 0) instead of (cx1, cx2 ). With the usual…

A: The multiplication cx where x∈ℝ2 is defined as cx=cx1, 0 because x=x1, x2 where x1 and x2 belong to…

Q: 5) Suppose that W1 < R" and W2 4 R". Prove (W1 n W2) < R"

A:

Q: = (-10,6, –4) be in R and a be in R. Then , 36 , Let x ат — ).

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: Deduce from Q2 that if an integer N can be written as N = x² + ny² , and if a prime number q | N can…

A: We will use standard division algorithms to deduce the given statement.

Q: リ ー上 5, Use the inverse imatirice s tofind and (24) 22 3 ミ 3. 3. 3 -2

A:

Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

A:

Q: -5² + 3(¯5)² 50 O -50 O 49 O -49

A: