Test for consistency and solve the equation | Linear algebra | Part 6

Linear Algebra | Test for consistency and solve the equation | 8 Problems:    • Linear Algebra | Test for consistency and ...  

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1️⃣ Test for consistency and solve the equation | Linear algebra | Part 1
🔗    • Test for consistency and solve the equatio...  

2️⃣ Test for consistency and solve the equation | Linear algebra | Part 2
🔗    • Test for consistency and solve the equatio...  

3️⃣ Test for consistency and solve the equation | Linear algebra | Part 3
🔗    • Test for consistency and solve the equatio...  

4️⃣ Test for consistency and solve the equation | Linear algebra | Part 4
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5️⃣ Test for consistency and solve the equation | Linear algebra | Part 5
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6️⃣ Test for consistency and solve the equation | Linear algebra | Part 6
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7️⃣ Test for consistency and solve the equation | Linear algebra | Part 7
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8️⃣ Test for consistency and solve the equation | Linear algebra | Part 8
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📘 Show that the System has No Solution | Inconsistent System | Linear Algebra
In this video, we prove that the given system of linear equations does not possess any solution (i.e., it is inconsistent) using the Rank Method.
We form the augmented matrix, apply Elementary Row Transformations (ERTs), compare the ranks of the coefficient matrix and augmented matrix, and conclude why the system has no solution.
A crucial problem type for VTU, BSc, BCA, Diploma, and many university exams.

📝 Question
Show that the following system of equations does not possess any solution:
5x + 3y + 7z = 5
3x + 26y + 2z = 9
7x + 2y + 10z = 5
(We use the Rank Method → Augmented matrix → ERTs → Inconsistency test.)

🎯 Who Should Watch This Video? (VTU – Latest CBCS/NEP)
✔ 1BMATS101 – Calculus & Linear Algebra (Module 3)
✔ 1BMATE101 – Differential Calculus & Linear Algebra (Module 5)
✔ 1BMATM101 – Differential Calculus & Linear Algebra (Module 4)
✔ 1BMATC101 – Differential Calculus & Linear Algebra (Module 5)
✔ BMATS101 / BMATE101 / BMATM101 / BMATC101 – Linear Algebra (Module 5)
✔ Ideal for BSc, BCA, Diploma & Degree students learning:
• Systems of Linear Equations
• Consistency & Inconsistency Tests
• Rank of a Matrix
• Augmented Matrix Method
• Elementary Row Transformations (ERTs)
• Echelon Form & RREF
Useful for exam revision, concept clarity, and last-minute preparation across all universities.

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