Let A₁ € Rmxn and A2 € Rnxn for arbitrary positive integers m and n. Suppose that A2 is non-singular. If we let A = show that ||A¹|| ≤ ||A₂¹||. [A] ER(m+n) xn 9

Q: Let X - N(2, 4). Calculate P[X2 – 4X < 4].

A: P(X2-4X≤4)=0.7602

Q: 2. Show that for any real number c, there is exactly one integer in the interval (c,c + 1].

A: As per guidelines, I can do only first question.

Q: 1. Find the Laplace transform of the function f(t) = eat[a cos(Bt) + b sin(3t)].

A:

Q: Let a and d be integers. Prove that if d|(8a+7)and d|(5a+4), then d|3

A:

Q: Prove the statement if it is true, and give a counterexample if it is not true. a. For every real…

A: Both the subparts are solved with explanation.

Q: Let f(x) = Ax² + Bx + C where A, B and C are real numbers. Prove that if f(x) is an integer whenever…

A:

Q: Prove that if |x-1| < 1, then x² - 2x + 5| < 8.

A:

Q: Show that ACB implies |A|≤|B|.

A:

Q: a) Prove that |x| ≤ 2 implies that |x² − 4| ≤ 4|x − 21.

A: To prove the given statement, let's break it down into a few steps: Starting with the assumption…

Q: prove for every positive real number x that 1+1/x2>=1/x+1/x3.

A: To prove: 1+1x2≥1x+1x3; for everypositive real number x.