Row × column: how one entry of a product is madeपंक्ति × स्तंभ: गुणनफल की एक प्रविष्टि कैसे बनती हैRow × column: product ki ek entry kaise banti hai

NCERT 3.4.5 · Class 12 Maths · Chapter 3 · interactive diagram

Parts and what they mean

• Row 2 of C: (0, 3, 4) (C की पंक्ति 2: (0, 3, 4)) — Its 3 numbers pair up, in order, with the 3 numbers of the chosen column of D.
• Column 1 of D: (2, −1, 5) (D का स्तंभ 1: (2, −1, 5)) — Top meets first, middle meets second, bottom meets third.
• Entry (2, 1) of CD = 17 (CD की प्रविष्टि (2, 1) = 17) — Row 2 of C with column 1 of D: 0(2) + 3(-1) + 4(5) = 17. It sits in row 2, column 1 of CD.
• Multiply pairs, then add (जोड़ियों का गुणा, फिर योग) — c_{21} = a_{21}b_{11} + a_{22}b_{21} + a_{23}b_{31} = 0 - 3 + 20 = 17.
• Matrix C (2 \times 3) (आव्यूह C (2 \times 3)) — C = \begin{bmatrix} 1 & -1 & 2 \\ 0 & 3 & 4 \end{bmatrix} — 3 columns.
• Matrix D (3 \times 2) (आव्यूह D (3 \times 2)) — 3 rows — the same as the 3 columns of C, so CD is defined.
• Product CD (2 \times 2) (गुणनफल CD (2 \times 2)) — CD = \begin{bmatrix} 13 & -2 \\ 17 & -13 \end{bmatrix}: rows of C, columns of D.
• When is AB defined? (AB कब परिभाषित है?) — Columns of the first = rows of the second. The outer numbers give the order of the product.
• Entry rule (प्रविष्टि का नियम) — c_{ik} = \sum_{j} a_{ij} b_{jk}.

Original diagram drawn by Simple Learning Hub, based on NCERT 3.4.5. Report a mistake