Use Gram-Schmidt to find q1, q2, q3 (orthonormal) as combinations of a, b, c (independent columns). Then write A as QR: [1 2 47 A = |0 0 5 = 0 3 6 QR

Q: 2sin2t=4sint+6 [0,2pi)

A: Answer and explanation is given below..

Q: verify that A(B + C) = AB + AC

A: Now,

Q: Let_Z1 = 3 + i and Z2 = 5 + 2 i . Find 2 Z1 /( Z1 - Z2) - (14/5)-2 i O (14/5) + 2i O - (14 / 5) + (…

A: Topic = Complex number

Q: (b) Let P = . Express the product PQ as a linear combination of the columns of P. -1 4

A: let P=1235-14 and Q=7-96 Then we have to find the product of PQ as a linear combination of the…

Q: Ifv = [ -2, 4], compute and draw 2v, 1/2 v, and -2v.

A:

Q: Find (a) u × v, (b) v × u, and (c) v × v.…

A: Given : u =0,2,1v = 1,-3,4(a) u x v = ijk0211-34u x v =i 21-34    -j0114  +k021-3          = i(8+3)…

Q: Find the product AB if

A: Given: A=12-340-2 and B=5-420-16317058

Q: Express (a) v = 3t² + 5t – 5 as a linear combination of the polynomials: P, =t² + 2t +1, P, = 21² +…

A: Suppose is a vector space . Dimension of  vector space is 3. The standard basis of vector space is…

Q: A researcher claims that the proportion of smokers in a certain city is less than 22%. A random…

A:

Q: 223+-5 -j Suppose z1 = 2+ j, 2 = 3- j2 and z3 = -+j Evaluate %3D 2-a+3-j

A: Substitute the given values of z1,  z2, z3 in the given expression and simplify.…

Q: Find the LU factorization of A = A = 1 1 -3 0 9 3 -17 5 2

A:

Q: verify that (A + B) + C = A + (B + C)

A: Now,

Q: verify that (A + B)C = AC + BC

A: To verify that (A+B) C = AC + BC.

Q: Determine a best rank-1 approximation, A₁, to the matrix A with respect to the 2-norm. That is, find…

A: The given matrix is A=-211-105. We need to find the rank 1 approximation of the given matrix and…

Q: let v = (−2, 5) and w = (3, −2) Calculate 5w − 3v and 5v − 3w

A: Consider the given vectors. v=-2,5w=3,-2 Now, find the value of the vector 5w − 3v.…

Q: a) Find a (b + c) b) Find | a. (b+c) |. State its geometric interpretation. c) Find a vector that is…

A: a=3i-2j+k,b=-2i+j-4k,c=-i+j-3k

Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: Let z1 = -5 + 14i and z2 = 5 – i. Find z122 and (z1z2). 7122 (2122) ||

A:

Q: For the numbers 1, 2, 4, 6, 8 Compute:  SX   SX2   (SX) 2

A: Given data is1, 2, 4, 6, 8

Q: Diagonalize A = 12 0 2 1 0 00 - 3 and compute A2019

A:

Q: * = -2x y2

A:

Q: A = p + prt for r ( banking)

A:

Q: Suppose the second column of B is all zeros.  What can you say about the second column of AB?

A: If the second column of B is all Zeros, then the second column of AB will also be all Zeros.

Q: The Taylor series for f(x) = ln(x) at c=3 is > C (x – 3)*. | k=0

A:

Q: s Write the following polynomials as coefficient vectors: 2x3-3x2 + x +5 3x5+x2-4

A: Solution of the problem is:-

Q: find the Bezout coefficients and write the gcd (243,715) as a linear combination of 243 and 715

A:

Q: Evaluate the commutators [Lz, r²] and [Lz, p²] (where, of course, r² x² + y² +z? and p? = p? + p; +…

A: Given To evaluate the commutators Lz,r2 and Lz,p2 where r2=x2+y2+z2 and p2=px2+py2+pz2.