Singular Matrix Trick in 60 Seconds! 🔥 | JEE Matrices

 

❓ Concept

🎬 Singular Matrix Trick in 60 Sec | JEE Matrices

2×2 matrix dikhi?
Aur question bole “singular”?

👉 Bas ek chhoti si identity yaad rakh lo —
baaki saara game automatic ho jaata hai 🔥

---

🖼️ Concept Image

---

✍️ Short Explanation

JEE mein “singular matrix” ka matlab definition-based hota hai.
No heavy algebra, no tricks — sirf determinant logic.

---

🔹 Step 1 — Singular Matrix Meaning (CORE RULE 💯)**

A matrix is singular

$$⟺$$

its determinant is zero.

📌 Yeh rule har order ke matrix ke liye true hai.

---

🔹 Step 2 — 2×2 Determinant Formula (MOST IMPORTANT 🔥)**

For a 2×2 matrix:

$$\begin{pmatrix} a & b\\ c & d \end{pmatrix}$$

Determinant:

$$|A| = ad - bc$$

So,

$$\boxed{\text{Matrix is singular } \Longleftrightarrow ad = bc}$$

👉 Bas yahi identity poore chapter ko control karti hai.

---

🔹 Step 3 — What These JEE Questions Are REALLY Doing

Typical JEE statement:

“Elements are chosen from a given set…”

Meaning:

• Choose values of $a, b, c, d$

• Check kab ad = bc ho raha hai

📌 Jitne combinations satisfy karein
👉 utni singular matrices

No need to calculate inverse, rank, eigenvalues —
sirf determinant condition check karo.

---

🔹 Step 4 — Important Insight (WRITE THIS BOLD 🧠)**

If two rows are proportional → matrix is singular
If two columns are proportional → matrix is singular

Why?

• Proportional rows/columns ⇒ $ad = bc$ automatically

• Determinant zero ho jaata hai

---

Example Idea (NOT solving, only concept):

$$\begin{pmatrix} 2 & 4\\ 1 & 2 \end{pmatrix}$$

Second row = $\tfrac{1}{2}$ × first row
👉 Rows proportional
👉 Determinant = 0
👉 Matrix singular

📌 Aise patterns ko pehchaan lo — counting fast ho jaati hai.

---

🔹 Step 5 — How JEE Tests This Concept

JEE usually asks:

• Count number of singular matrices

• Identify whether matrix is singular

• Use proportionality logic to eliminate options

👉 Always reduce the problem to:

$$ad = bc$$

---

⭐ ONE-LINE SUMMARY BOX (WRITE THIS)

2×2 matrix is singular ⇔ $ad = bc$

Is ek line ko yaad rakh liya,
👉 singular matrix ka poora game easy 🔥

---

✅ Final Takeaway

🧠 Singular Matrix Master Rule

• Determinant = 0 ⇒ singular

• 2×2 case ⇒ $ad = bc$
  

• Proportional rows/columns ⇒ instant zero determinant

Is concept ko pakad liya,
👉 Matrices ke “counting + theory” questions JEE mein free marks ban jaate hain 😎