Final answer:
The use of an elementary row operations calculator is suitable for solving matrix-based systems of linear equations, which is true. The statement regarding vectors forming a right-angle triangle with components, the unit consistency in E = mc², expressing 2-D vectors with components, and the Pythagorean theorem to find resultant vector length are all true.
Step-by-step explanation:
The statement that an elementary row operations calculator is suitable for solving systems of linear equations represented by matrices is True. Elementary row operations are critical when using methods like Gaussian elimination to solve systems of equations. Such calculators can assist in performing row operations to achieve a row-echelon form or reduced row-echelon form of a matrix, which can simplify the process of finding solutions.
A vector can indeed form the shape of a right-angle triangle with its x and y components, which is True. This is because the components of the vector act as the perpendicular sides of the triangle, and the vector itself represents the hypotenuse.
It is True that we can use the relationships F = ma (force is equal to mass times acceleration) and E = Fd (energy is equal to force times distance) to show that both sides of the equation E = mc² have the same units. The unit of force (F) is Newtons (N), which is kg·m/s², and distance (d) is in meters (m), so energy (E) is in joules (J), which is kg·m²/s², the same units as mc² where m is mass in kilograms (kg) and c is the speed of light in m/s.
Every 2-D vector can be expressed as the product of its x and y-components, which is expressed as Ax = A cos θ and Ay = A sin θ, making the statement True.
Finally, when two vectors are at right angles to each other, we can indeed use the Pythagorean theorem to calculate the length of the resultant vector, so this statement is also True.