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Given $A=\left[\begin{array}{rr}{4} & {-6} \\ {-8} & {12} \\ {6} & {-9}\end{array}\right],$ find one nontrivial solution of $A \mathbf{x}=\mathbf{0}$ by inspection.

Inspect how the columns $a_{1}$ and $a_{2}$ of $A$ are related. The second column is $-3 / 2$ times the first. Put another way, $3 a_{1}+2 a_{2}=0 .$ Thus $\left[\begin{array}{l}{3} \\ {2}\end{array}\right]$ satisfies $A x=0$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 5

Solution Sets of Linear Systems

Introduction to Matrices

Campbell University

Oregon State University

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Lectures

01:32

In mathematics, the absolu…

01:11

03:51

Given $A=\left[\begin{arra…

00:41

If $Q(a)=6 a-1,$ find $a$ …

02:01

Solve. If no solution exis…

19:49

Determine the general solu…

00:42

In the following exercises…

00:40

Use a check to determine w…

00:47

Determine if the given val…

01:31

01:09

Tell whether the given num…

03:17

$$\begin{aligned}-9-a …

this this problem work even the Matrix or negative six connective eight and 12 and six active at night. Now we need to find the one country solution off X equals zero system. You were considering this homogeneous system. X equals zero. So we first do the Calgary gushing elimination. We observed that the second rule is actually connected with twice next two times, the times the first roll. So I can just, ah, cancel the second rule by by adding the first roll times too. So that's for an active six and 00 I also observed that weekend, uh, he was the third role. Here's the 33rd World minus, uh, find out of 33 minus 3/2 off the first rule. So that is, uh, 3/2 off for that is six and six minus 60 and 3/2 off. Next six will be next. Nyah, I reckon I minus neck tonight is zero. So finally we have I only we have 34 x one minus six x for X two is zero. So to find a nontrivial solution, we just take X one as three and next to as to so three times worries 12 and two times six is 12 and 12 months minus well, zero. So we're done

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In mathematics, the absolute value or modulus |x| of a real number x is its …

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