Investigate For values of a & b the System has Unique Solution, Infinite Solution, No solution

#Investigate for #what values of a and b the equations
X+2Y+3Z=4, X+3Y+4Z=5, x+3y+az=b
Have i) #No Solution, ii) #Solution, iii) #Infinite Solutions
Dear students, based on students request , purpose of the final exams, i did chapter wise videos in PDF format, if u are interested, you can download Unit wise videos by clicking the below links
Unit 1:ODE First order Differential Equations
drive.google.com/file/d/1NTal...
Unit 2: Higher order DE.
drive.google.com/file/d/1NYx2...
Unit 3: Multiple Integrals
drive.google.com/file/d/1Nhv_...
Unit 4:Vector Differential Calculus
drive.google.com/file/d/1NjRS...
Unit 5:Vector Integral Calculus Part 1
drive.google.com/file/d/1O-xA...
Unit 6: Vector Integral Calculus Part 2
drive.google.com/file/d/1O1gS...
Unit 7: Special Functions
Beta & Gamma Functions
drive.google.com/file/d/113Sb...
Unit 8: Functions of Single Variables
drive.google.com/file/d/19SN5... Please subscribe to my Channel - / @teameducationmathematics
Unit 1: First Order ODE- Playlist
czcams.com/users/playlist?list...
Unit 2:ODE of Higher Order- Playlist
• Linear Differential Eq...
Unit 3: Multi Variable Calculus-(Integration)-Playlist
/ watch v=lUzFBROiTFc&list=PL3b73JEqFpKbsEkzC7fYYgMxY7z2Gn28h
Unit 4: Vector Differentiation-Playlist
• Introduction to the Ve...
Unit 5: Vector Integration-Playlist
• Line integral definiti...

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Find the values of a and b so that the equations x + y + z = 3 , x + 2y + 2z = 6 , x + ay + 3z = b have i)No solution ii)A unique solution iii)An infinite number of solutions.

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how do you do this easily without using matrices?

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