Question

The area of the parallelogram formed by vectors a=(−1,3,1) and b=(1,2,0), rounded to one decimal, is:

Select one:

a. 5.4

b. 5.5

c. -6.0

d. none of above

Find the component of the vector with initial point (2,−1,1) and terminal point (4,3,−6):

Select one:

a. (2,4,−7)

b. (6,3,−5)

c. (8,−3,−6)

d. (−2,−4,7)

Determine whether the statement is True or False:

The sum of two invertible matrices of the same size must be invertible.

Select one:

a. True

b. False

Determine whether the statement is True or False:

For all square matrices A and B of the same size, it is true that (A+ B)²=A²+2AB+B².

Select one:

a. True

b. False

Let u=(2, −2, −1) and v=(−2, 1, −1). Find u×v.

Select one:

a. (3, −4, −2)

b. (3,4, 2)

c. (3,4, −2)

d. (−3,4, 2)

Determine whether the statement is True or False:

For all square matrices A and B, it is true that det(A+B)= det(A)+det(B)

Select one:

a. True

b. False

Determine whether the statement is True or False:

The zero space is a subspace of Rⁿ, for any n.

Select one:

a. True

b. False

Which of the following vector sets does not span R²:

Select one:

a. (-1,2), (2,-4)

b. (1,1), (0,1)

c. (-1,-1), (-2,3)

d. (0,1), (2,-3)

Determine whether the statement is True or False:

If A and B are matrices of the same size, and k is a constant, then (kA+B)^T= kA^T+B ^T.

Select one:

a. True

b. False

Find the coordinate vector of x relative to the basis S={u,v} for R²:

u=(0,2), v=(1,1), x=(2,4).

Select one:

a. (1,2)

b. (0,1)

c. (2,-1)

d. none of above

Determine whether the statement is True or False:

Any set of four linearly independent vectors in R⁴ forms a basis for R⁴.

Select one:

a. True

b. False

Determine whether the statement is True or False:

If A is a square matrix, and the linear system Ax=b has a unique solution, then the linear system Ax=c also must have a unique solution.

Select one:

a. True

b. False

Determine whether the statement is True or False:

If one vector is a scalar multiple of another vector, then the two vectors are collinear.

Select one:

a. True

b. False

Determine whether the statement is True or False:

Two n×n matrices A and B are inverses of one another if and only if AB=BA=0.

Select one:

a. True

b. False

Determine whether the statement is True or False:

If A and B are matrices such that AB is defined, then it is true that (AB)^T=A^TB^T

Select one:

a. True

b. False

Let u = (2, −1) and v = (1, 1). Find the angle between u and v in radians (round to one decimal).

Select one:

a. 71.6

b. 1.2

c. 0.3

d. -1.2

3 vectors (−1, 2, −3), (3, −7,8), and (2, −4,6) span:

Select one:

a. R²

b. R¹

c. R⁰

d. R³

Determine whether the statement is True or False:

If A is an nxn matrix, then the linear system Ax=2x has a unique solution if and only if A-2I_n is an invertible matrix.

Select one:

a. True

b. False

Determine whether the statement is True or False:

For all square matrices A and B, it is true that det(AB)= det(A)det(B)

Select one:

a. True

b. False

Determine whether the statement is True or False:

If A and B are invertible matrices of the same size, then AB is invertible and

(AB)^-1=A^-1B^-1.

Select one:

a. True

b. False

Determine whether the statement is True or False:

A square matrix A is invertible if and only if the reduced row echelon form of A is I_n.

Select one:

a. True

b. False

Which of the following subsets is not the basis for P₂:

Select one:

a. x² –2, x²+1, 3

b. x², x+2, –2

c. –x²+2, x-3, 1

d. x²–x, 3x, 4

Determine whether the statement is True or False:

The sum of a diagonal matrix and a lower triangular matrix is a diagonal matrix.

Select one:

a. True

b. False

Determine whether the statement is True or False:

A diagonal matrix is invertible if and only if all of its diagonal entries are positive.

Select one:

a. True

b. False

Determine whether the statement is True or False:

For all square matrices A and B of the same size, it is true that A² −B²=(A−B)(A+B)

Select one:

a. True

b. False

Let u=(2, −2, −1) and v=(−2, 1, 0.5). Find the norm of u+2v.

Select one:

a. 2

b. −2

c. 0

d. 1.25

Let u = (2, −2, −1) and v = (−2, 1, −1). Find the distance between these two vectors (round to one decimal).

Select one:

a. 3.0

b. 4.1

c. 5.0

d. 4.0

Find the values k for which the matrix is invertible:

−

Select one:

a. k ≠ −6; 1 (all other real numbers)

b. k ≠ 6; −1 (all other real numbers)

c. All real numbers

d. k ≠ 2; 3 (all other real numbers)

Answer 1

aoluleon :- of of cross parallelogram = magnitude product -431 -13 I 2 A = 1ăx51 I product Ace XXX ã x 5= (-2, 215) 10-2, 1-0, -352) 10x 51- J (2) 2 + (1 j2 +65 32 1 (-2, 215) - Juti +25 = 530 =155] Ame uti +25