Transpose: rows become columnsपरिवर्त: पंक्तियाँ स्तंभ बन जाती हैंTranspose: rows columns ban jaati hain

NCERT 3.5 · Class 12 Maths · Chapter 3 · interactive diagram

Parts and what they mean

• Row 1 (3, 5) → column 1 (पंक्ति 1 (3, 5) → स्तंभ 1) — The first row of A becomes the first column of A′.
• Row 2 (√3, 1) → column 2 (पंक्ति 2 (√3, 1) → स्तंभ 2) — The second row of A becomes the second column of A′.
• Row 3 (0, −1/5) → column 3 (पंक्ति 3 (0, −1/5) → स्तंभ 3) — The third row of A becomes the third column of A′.
• Matrix A (3 \times 2) (आव्यूह A (3 \times 2)) — A = \begin{bmatrix} 3 & 5 \\ \sqrt3 & 1 \\ 0 & \frac{-1}{5} \end{bmatrix}
• Transpose A′ (or Aᵀ), 2 \times 3 (परिवर्त A′ (या Aᵀ), 2 \times 3) — Rows and columns interchanged. Transposing again gives back A: (A')' = A.
• Rows ↔ columns (पंक्तियाँ ↔ स्तंभ) — Each row, read left to right, is written as a column, top to bottom.
• (i, j)th element of A′ (A′ का (i, j)वाँ अवयव) — The (i, j)th element of A' is the (j, i)th element of A.
• Order flips (कोटि पलट जाती है) — 3 \times 2 becomes 2 \times 3.

Original diagram drawn by Simple Learning Hub, based on NCERT 3.5. Report a mistake