https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/v/minors-and-cofactors 2025-06-25T04:37:22.958747522Z उपसारणिक तथा सहखंड In this video, we learn how to find minors and cofactors corresponding to the elements of a determinant. We start off with minors and then understand how we can get cofactors from minors. We look at the multiplying factor and how the power of -1 works. We then practice finding minors and cofactors for a given determinant. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw उपसारणिक तथा सहखंड In this video, we learn how to find minors and cofactors corresponding to the elements of a determinant. We start off with minors and then understand how we can get cofactors from minors. We look at the multiplying factor and how the power of -1 works. We then practice finding minors and cofactors for a given determinant. https://cdn.kastatic.org/ka-youtube-converted/UOp4snBFUes.mp4/UOp4snBFUes.mp4 450 आव्यूह का सहखंडज https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/v/finding-determinants-using-cofactors 2025-06-25T04:37:22.958747522Z सहखंड का प्रयोग करके सारणिकों को ज्ञात करना In this video, we learn how to find determinants using cofactors. We first refresh our understanding of minors and cofactors. We then compare the terms in the expression for the determinant with cofactors of the same determinant. Finally, we look at what happens if we pair elements with cofactors from a different row and try to build an intuition for the result. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सहखंड का प्रयोग करके सारणिकों को ज्ञात करना In this video, we learn how to find determinants using cofactors. We first refresh our understanding of minors and cofactors. We then compare the terms in the expression for the determinant with cofactors of the same determinant. Finally, we look at what happens if we pair elements with cofactors from a different row and try to build an intuition for the result. https://cdn.kastatic.org/ka-youtube-converted/tNRZGrH4Kg4.mp4/tNRZGrH4Kg4.mp4 376 आव्यूह का सहखंडज https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/v/adjoint-of-a-matrix 2025-06-25T04:37:22.958747522Z आव्यूह का सहखंडज In this video, we learn how to find the adjoint of a given matrix. We first find minors corresponding to each element. From the set of minors, we build cofactors. Taking the transpose of the matrix of cofactors gives us the adjoint matrix. We practice finding the adjoint of a given 3x3 matrix. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw आव्यूह का सहखंडज In this video, we learn how to find the adjoint of a given matrix. We first find minors corresponding to each element. From the set of minors, we build cofactors. Taking the transpose of the matrix of cofactors gives us the adjoint matrix. We practice finding the adjoint of a given 3x3 matrix. https://cdn.kastatic.org/ka-youtube-converted/yNpT9Da0KDs.mp4/yNpT9Da0KDs.mp4 247 आव्यूह का सहखंडज https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:determinants-ncert-new/x7ce8ca9c5869750b:adjoint-of-a-matrix/v/intuition-behind-product-with-adjoint 2025-06-25T04:37:22.958747522Z सहखंडज के साथ गुणन के पीछे की सामान्य समझ In this video, we understand what happens when we multiply a matrix with its adjoint. We realise that the resultant is equal to the determinant of the matrix multiplied by the identity matrix irrespective of the order of the multiplication. We finally try to build some intuition for why this works. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सहखंडज के साथ गुणन के पीछे की सामान्य समझ In this video, we understand what happens when we multiply a matrix with its adjoint. We realise that the resultant is equal to the determinant of the matrix multiplied by the identity matrix irrespective of the order of the multiplication. We finally try to build some intuition for why this works. https://cdn.kastatic.org/ka-youtube-converted/cLRjo4dtQdU.mp4/cLRjo4dtQdU.mp4 628 आव्यूह का सहखंडज