Linear Algebra Answers

Q4.

The value of x "\\in" R^4

such that (4, 3, - 3, 2) + 3x = (7, -3, 3, 2) is

(1) x = (4, -4, 3, 0)

(2) x = (4, - 4, 3, 0)

(3) x = (1, -2, 0, 0)

(4) None of the given answers is true.

Q5.

Let W be a subset of R^3 defined as

W = (x, y, z) "\\in" R^3: 2x + y - z - 1 = 0.

Then

(1) W is a subspace of R^3

(2) W is closed under scalar multiplication

(3) W is not a subspace of R^3

(4) None of the given answers is true.

Q6.

The set of differentiable real-valued functions f on the interval (0,3) such that f'(2) = "\\alpha" is a subspace of R^(0,3). The value of must be

(1) negative

(2) positive

(3) zero

(4) None of the given answers is true.

Q1.

Consider the sets

A = {x "\\in" Z : x = 2 (y - 2) for some

y "\\in" Z} and B = {x "\\in" Z : x = 2z for some z "\\in" Z}. Then

(i) A and B are equal,

(ii) A {\displaystyle \subsetneq } B,

(iii) B {\displaystyle \subsetneq } A

(1) (i) only

(2) (ii) only.

(3) (iii) only

(4) None of the given answers is true.

Q2.

Consider a function f: R → R^+ defined as f(x) =e^x: Then the image of S ={x ∈ R: 0 ≤ x^2 - 9} is

(i) (-∞; e^-3]U[e^3;∞);

(ii) [e^-3; e3^];

(iii)[e^3;∞)

(4) None of the given answers is true.

Q3.

The two distinct square roots of i is

(1) √2 + √2i and -√2 - √2i

(2) 2√2 + 2√2i and - 2√2 - 2√2i

(3)√2/2 + √2/2(I) and - √2/2 - √2/2(I)

(4) None of the given answers is true.

If the owner needs one employee for every 25 cups of coffee sold per hour, determine how many employees are required for the morning shift from 6 am to 1 pm?

Find the solution of the system of linear equation by using augmented matrix.

\left. \begin{array} { l } { x _ { 1 } - 2 x _ { 2 } = 0 } \\ { 3 x _ { 1 } + 4 x _ { 2 } = - 1 } \\ { 2 x _ { 1 } - x _ { 2 } = 3 } \end{array} \right.

find the inverse of this matrix

A= 1 3 5 4

7 2 9 6

find the inverse of this matrix by using Gausian method

A= 4X + 5Y = 6

X + 5Y = 3

Show that the set W = {(a, b, 0) : a, b ∈ F} is a subspace of V3(F).

3x1²+3x2²+3x3²+2x1x2+2x1x3-2x2x3

Find rank, index, signature and nature of the Quadratic form by reducing it into

Canonical form by orthogonal transformation 2x2 + 2y2 + 322 + 2xy - 4y2 - 42x.

{F} LA. find the minimal polynomial of the linear operator t : R³ "- R³" define by t (x,y,z) =(x+2y+3z, 4y+5z,6 z).is t