Let Ax^rightarrow = 0 be a homogeneous system of linear equations. Suppose x^rig

Question

Let Ax^rightarrow = 0 be a homogeneous system of linear equations. Suppose x^rightarrow _x1and x^rightarrow _2 are both solutions of Ax^rightarrow = 0 Verify that 2x^rightarrow _1 - 3x^rightarrow _2 is also a solution of Ax^rightarrow = 0. Let Ax^rightarrow = b^rightarrow be a system of linear equations for which b^rightarrow not equal to 0^rightarrow. Suppose x^rightarrow _1 and x^rightarrow _2 are both solutions of Ax^rightarrow = b^rightarrow Is it true that x^rightarrow _1 + x^rightarrow _2 is also a solution? Justify your answer. Let A = [1 1 -6 2 1 -8 3 1 -11] compute A^-1. Use a^-1 to solve the following system of linear equations: x_1 + x_2 - 6x_3 = 3 2x_1 + x_2 - 8x_3 = 3 x_1 + x_2 - 11x_3 = 1

Explanation / Answer

a) We know Ax =0 system of equation

and x1 is aolution vectors : Ax1 =0

and so is A2x1 =0 ----(1)

x2 is solution vector : Ax2=0

so is A(-3x2) =0 ---(2)

So, add two equations we get: A2x1 + A(-3x2) =0

A( 2x1 -3x2) =0

So, 2x1 -3x2 is also a solution

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.