Final answer:
The augmented matrix encapsulates all essential info for the given linear system; vector components can form a right angle triangle and use the Pythagorean theorem to find the resultant vector; the direction of a resultant vector depends on the magnitude and direction of its components.
Step-by-step explanation:
The augmented matrix for a linear system does indeed contain all the essential information from the system, so the answer to the first question would be A. True. An augmented matrix is a compact way of representing the coefficient matrix of the system along with the constants from the equations, effectively capturing all the necessary information for solving the system.
When it comes to vectors, if we decompose a vector into its x and y components, these components can indeed form a right angle triangle with the original vector being the hypotenuse, so the answer is A. True. This leads us to the application of the Pythagorean theorem, which can be used to calculate the length of the resultant vector if the two vectors are at right angles to each other.
The direction of the resultant vector is dependent on both the magnitude and direction of the added vectors, indicating that the statement is True. The amplitude of waves does add up if they are in phase or propagating along the same line, so the statement is True. Furthermore, the amplitude of one wave is affected by another only if they interfere with each other, which generally requires them to be aligned, so that statement is also True.
A simulation model would be ideal for representing systems, including simple linear ones, that are mathematically complex. Lastly, if only the angles of two vectors are known, without magnitude, we can't find the resultant vector's angle. But if we know the angles and the magnitude of one of those vectors, we can indeed find the magnitude and direction of the resultant vector.