In Problems 26 − 28 , use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. 1 2 + 4 2 + 7 2 + ⋯ + ( 3 n − 2 ) 2 = 1 2 n ( 6 n 2 − 3 n − 1 )
In Problems 26 − 28 , use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. 1 2 + 4 2 + 7 2 + ⋯ + ( 3 n − 2 ) 2 = 1 2 n ( 6 n 2 − 3 n − 1 )
Solution Summary: The author explains how to prove the given statement by using the mathematical induction for all natural numbers.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY