Determine whether each of the sets below is a basis for R³. Explain any theorems or results you rely on in your answers. (a) X = {(1, 1, 1), (1, −1, 1), (1, 1, −1)}. (b) Y = {(1, −2, −1), (2, −3, 1), (5, —8, 1)}. (c) Z = {(1, 0, 1). 0), (0,3,3)}.

Q: -5 7 Eхample 61. Find the adjoint of A = -2 and show that A (adj. A)=|A| I.

A:

Q: Find the value of t so that t t = 6 -1 t

A: tt-1t=6

Q: Find JA|, |B|, A + B, and |A + BỊ. Then verify that |A| + |B| # |A 1 6 [o 1 -1 A = 1 -1 0 B = 6 1 1.…

A:

Q: Z2 in H = {0,4,8} find all left cosettes

A:

Q: Q1: Sketch the signals A. x(t) x(-1/2) A CL x(2(1+2)) x(−1+1) Ates Ades 0 2 B. 2 x(t) 0 1 x (3t),…

A: Given data:- Part A=   Part B

Q: X1 3x2 + 5x3 + 15x4 T(x) = |3x₁ + 8x2 − 2x3 − 23x4 4x17x2 + x3 - 16x4

A:

Q: If 7,=-4-J5 Z2= -3 +j2, and Zg =2-3, what is Re (23-2 7, + 23 Note : z* is the complex conjugate Of…

A:

Q: 1 cartesian form of (9-3j)³ is 2.1047-j0.2266

A:

Q: Find a + b, 2a + 3b, lal, and la - bl. a = i +3j - 4k, b = -3i -j + 6k a+b= 2a + 3b = |a| = |a - b|…

A: Given vectors  a = i + 3j - 4kb = -3i - j + 6k

Q: Evaluate the complex numbers j(3 – j4)* (-1+ j6)(2 + j)² (a) z1 1 +j 4 – j8 11/2 (b) Z2

A:

Q: Suppose ū=i- j, v = −2i + 4j+3k and w = -5i + 4j. Compute the following values: |u| + |v|=| |-6u|…

A: Since you have posted a multi subparts question according to guidelines I will solve first(1,2,3)…

Q: If Z=x+iy and 3x+(3x-y)i=4-6i then Z . * -4/3+10i O 4/3-10i O 4/3+10i -4/3-10i

A:

Q: nd a, b e R such that 4 5 a + bi 1- 2i i - 2 i- 2

A:

Q: tan(z1) 0.9947 + 0.1462i 0.0364 1.0047i

A: The definition of tangent function for complex number is tanz=e2iz-1i(e2iz+1). Use 4-2i for z1 and…

Q: Find curl (2z i + 3x j+ 2y k). curl (2z i + 3x j+ 2y k) = )i + ( i )j + ( i i )k

A:

Q: Show mathematically that (10-6) is not independent of (10-1),(10-3), and (10-4).

A: We can write (10  -6) as:

Q: How many solutions does Ax = [1]   have?

A:

Q: Fill in the blanks with the appropriate expressions/values that are needed to solve the equation by…

A: The given expression is: x2+10x+26=0

Q: Find a fourth degree polynomial that has zeros of 1, -3, 2i.

A:

Q: z1= 11-15i z2= 13+2i z3= 5+31i 24= 9-25i 25= 10-10i 26= 3+4i 4(z1 – z2) , (Z5 – z6) _ (z2 + z3)³ +…

A: To reduce to a+bi

Q: 3. Find all real numbers t for V = (20 t,4t - 4,5t², t²) are orthogonal. - which = (1,5t,-4t, t³)…

A:

Q: T: ([₂]) = 3x1 +4x2 x1 - 2x2 4x1

A:

Q: Find |A|, [B], A + B, and JA + BỊ. Then verify that |A| + |B| = |A + BỊ. 1 7 A = 1 -1 0 0 1 -1 B = 7…

A: We can solve this as follows:

Q: Find JA|, IB|, A + B, and |A + BỊ. Then verify that |A| + |B| # |A + B|. 15 0 1 -1 A = 1 -1 0 B = 5…

A: topic - determinant and matrices

Q: B) If A=0 0 |1 0 01 ,1+0 1 0 prove that A- =(A² + (C + A) + (D + I) 0 0 1 1 C and D are constant 014

A: In this question we have to prove A-1=16A2+C*A+D*I where C and D are constant