Answer:
A. False
B. False
C. True
D. True
E. True
F. True
Explanation:
A. The equation Ax=b is referred to as a matrix equation and not vector equation.
B. If the augmented matrix [ A b ] has a pivot position in every row then equation Ax=b may or may not be consistent. It is inconsistent if [A b] has a pivot in the last column b and it is consistent if the matrix A has a pivot in every row.
C. In the product of Ax also called the dot product the first entry is a sum of products. For example the the product of Ax where A has [a11 a12 a13] in the first entry of each column and the corresponding entries in x are [x1 x2 x3] then the first entry in the product is the sum of products i.e. a11x1 + a12x2 +a13x3
D. If the columns of mxn matrix A span R^m, this states that every possible vector b in R^m is a linear combination of the columns which makes the equation consistent. So the equation Ax=b has at least one solution for each b in R^m.
E. It is stated that a vector equation x1a1 + x2a2 + x3a3 + ... + xnan = b has the same solution set as that of the linear system with augmented matrix [a1 a2 ... an b]. So the solution set of linear system whose augmented matrix is [a1 a2 a3 b] is the same as solution set of Ax=b if A=[a1 a2 a3] and b can be produced by linear combination of a1 a2 a3 iff the solution of linear system corresponding to [a1 a2 a3 b] takes place.
F. It is true because lets say b is a vector in R^m which is not in the span of the columns. b cannot be obtained for some x which belongs to R^m as b = Ax. So Ax=b is inconsistent for some b in R^m and has no solution.
Answer: The correct answer is a.
Explanation:
Electromagnetic wave is a wave in which the magnetic field and the electric field are perpendicular to each other.
Both fields are directed in the direction of the propagation of the electromagnetic wave. It travels with the speed of the light.
The motion of the electric field produces both electric field and the magnetic field.
The electromagnetic waves are produced when an electric charge vibrates or accelerates.
Therefore, the correct option is (a).
Answer:
angle = 18.40 degree
Explanation:
given data
force = 95 N
distance = 0.50 m
torque = 15 N · m
to find out
angle between the wrench handle and the direction of the applied force
solution
we will apply here torque equation that is express as
torque = distance × force × sin(θ) ...................1
put here value we will get angle that is
15 = 0.50 × 95 × sin(θ)
sin(θ) = 0.315789
θ = 18.40 degree
I agree with you the answer is A
