https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/v/properties-of-transpose-of-the-matrices 2025-06-25T04:37:22.958747522Z आव्यूहों के परिवर्त के गुणधर्म In this video, we learn about the properties of a transpose of a matrix. We first look at the properties and then dive deeper to understand how they work. We look at these properties - Transpose of a transpose, Multiplying with a scalar, Transpose of a sum, and Transpose of a product. We finally solve a practice problem to test our knowledge. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw आव्यूहों के परिवर्त के गुणधर्म In this video, we learn about the properties of a transpose of a matrix. We first look at the properties and then dive deeper to understand how they work. We look at these properties - Transpose of a transpose, Multiplying with a scalar, Transpose of a sum, and Transpose of a product. We finally solve a practice problem to test our knowledge. https://cdn.kastatic.org/ka-youtube-converted/FhtU5KUB3oA.mp4/FhtU5KUB3oA.mp4 579 आव्यूह का परिवर्त (a matrix of transpose) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:matrices-ncert-new/x7ce8ca9c5869750b:transpose-of-matrix/v/symmetric-and-skew-symmetric-matrices 2025-06-25T04:37:22.958747522Z सममित आव्यूह और विषम सममित आव्यूह In this video, we talk about symmetric and skew symmetric matrices. We first look at examples of each and then understand the constraints on the elements. We then verify 2 results that work for sum and difference of a matrix and its transpose. We finally derive these results using properties of transpose of a matrix. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सममित आव्यूह और विषम सममित आव्यूह In this video, we talk about symmetric and skew symmetric matrices. We first look at examples of each and then understand the constraints on the elements. We then verify 2 results that work for sum and difference of a matrix and its transpose. We finally derive these results using properties of transpose of a matrix. https://cdn.kastatic.org/ka-youtube-converted/PdWVC5WaTXU.mp4/PdWVC5WaTXU.mp4 468 आव्यूह का परिवर्त (a matrix of transpose) https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/v/expressing-as-a-sum-of-symmetric-and-skew-symmetric-matrix 2025-06-25T04:37:22.958747522Z सममित आव्यूह और विषम सममित आव्यूह के योगफल के रूप मे व्यक्त करना) In this video, we leverage the results derived in the previous video to express any given matrix as a sum of a symmetric and a skew symmetric matrix. We first review these results. We add half of sum to half of difference to get the desired outcome. We finally practice a problem we express a 3x3 matrix as a sum of a symmetric and a skew symmetric matrix. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सममित आव्यूह और विषम सममित आव्यूह के योगफल के रूप मे व्यक्त करना) In this video, we leverage the results derived in the previous video to express any given matrix as a sum of a symmetric and a skew symmetric matrix. We first review these results. We add half of sum to half of difference to get the desired outcome. We finally practice a problem we express a 3x3 matrix as a sum of a symmetric and a skew symmetric matrix. https://cdn.kastatic.org/ka-youtube-converted/xo-ZChmfvSs.mp4/xo-ZChmfvSs.mp4 394 आव्यूह का परिवर्त (a matrix of transpose)