https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/defined-and-undefined-matrix-operations 2021-03-19T16:21:24Z Defined matrix operations Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Sal Khan video https://cdn.kastatic.org/googleusercontent/P6ZHMxo2YKBVx7evRA42gE4oLdC44-WS3_8cmsWLLuPBQs2viKFAdGsIV7sEctdKrpdEWmLcaMu-MyhGf-fGBsY Defined matrix operations Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. https://cdn.kastatic.org/ka-youtube-converted/O1-9f1g0OsI.mp4/O1-9f1g0OsI.mp4 212 Exploring properties of matrix multiplication https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/identity-matrix 2021-03-19T16:21:22Z Intro to identity matrix Just as any number remains the same when multiplied by 1, any matrix remains the same when multiplied by the identity matrix. Learn more from Sal. Sal Khan video https://cdn.kastatic.org/googleusercontent/M-dQFjdvi_C1MY4zwkHnVXfbRskqARCiv_iwSjEQ1NP4yKPL1hhKKG1RPTXBJ_h4GfkR_TNv8wFvSrOVkjaxePAp Intro to identity matrix Just as any number remains the same when multiplied by 1, any matrix remains the same when multiplied by the identity matrix. Learn more from Sal. https://cdn.kastatic.org/ka-youtube-converted/3cnIa0fYJkY.mp4/3cnIa0fYJkY.mp4 479 Exploring properties of matrix multiplication https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/identity-matrix-dimensions 2021-03-19T16:21:24Z Dimensions of identity matrix Sal explains why the identity matrix is always a square matrix, even though it works with non-square matrices. Sal Khan video https://cdn.kastatic.org/googleusercontent/cOU5cEbCWXkpErv2RgxQ9X92AoCaDnZ1CNs4fnifdks7AxC22XANB4r8ubvTxvswcLsdOfSax6iwN4_Fszl8Rnwf Dimensions of identity matrix Sal explains why the identity matrix is always a square matrix, even though it works with non-square matrices. https://cdn.kastatic.org/ka-youtube-converted/l7p1X5pdDoc.mp4/l7p1X5pdDoc.mp4 224 Exploring properties of matrix multiplication https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/commutative-property-matrix-multiplication 2021-03-19T16:21:23Z Is matrix multiplication commutative? Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). Sal Khan video https://cdn.kastatic.org/googleusercontent/WJR2HLZMFiOH6UEMJBxbFA4kAksb7KVyEteoWXm-tMbL6IcnVzmHPrqowjX9sAbnMyXzfCYgo6Otx8iq86bwVWcB Is matrix multiplication commutative? Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). https://cdn.kastatic.org/ka-youtube-converted/z-SU7P-gIoQ.mp4/z-SU7P-gIoQ.mp4 452 Exploring properties of matrix multiplication https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/associative-property-matrix-multiplication 2021-03-19T16:21:23Z Associative property of matrix multiplication Sal shows that matrix multiplication is associative. Mathematically, this means that for any three matrices A, B, and C, (A*B)*C=A*(B*C). Sal Khan video https://cdn.kastatic.org/googleusercontent/pmLLh5x1lgfZvgSJ0tcBps-WRAbPR55vRtP3I4cnQwijpNXwTR8pHIYvToKJNfJo1hRFLxbWThRSnO4U7J5jc-I Associative property of matrix multiplication Sal shows that matrix multiplication is associative. Mathematically, this means that for any three matrices A, B, and C, (A*B)*C=A*(B*C). https://cdn.kastatic.org/ka-youtube-converted/8Ryfe82DTcM.mp4/8Ryfe82DTcM.mp4 517 Exploring properties of matrix multiplication https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/zero-matrix 2021-03-19T16:21:22Z Zero matrix & matrix multiplication Just as any number multiplied by zero is zero, there is a zero matrix such that any matrix multiplied by it results in that zero matrix. Learn more from Sal. Sal Khan video https://cdn.kastatic.org/googleusercontent/i-6W_dqrs-9neFNYpv9PGKBR95MhQqjDY_uKtketTzFi90_TAT9tLgs5G3QHPMrhu4nAMhqKjXNS3Zs18ewF7eyQog Zero matrix & matrix multiplication Just as any number multiplied by zero is zero, there is a zero matrix such that any matrix multiplied by it results in that zero matrix. Learn more from Sal. https://cdn.kastatic.org/ka-youtube-converted/LOf8bfjiLow.mp4/LOf8bfjiLow.mp4 282 Exploring properties of matrix multiplication https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/matrix-expressions 2021-03-19T16:21:23Z Using properties of matrix operations Sal determines which of a few optional matrix expressions is equivalent to the matrix expression A*B*C. This is done using what we know about the properties of matrix addition and multiplication. Sal Khan video https://cdn.kastatic.org/googleusercontent/gJIXmhrbpBaOhbgnBXDJzKjNZoeZtDGDPp-mjIuCzkhsznd006UQzPaBH5t0cyyUMbCkHYQBV1W6h2EQfpZk42UaYw Using properties of matrix operations Sal determines which of a few optional matrix expressions is equivalent to the matrix expression A*B*C. This is done using what we know about the properties of matrix addition and multiplication. https://cdn.kastatic.org/ka-youtube-converted/OjF765iVuF8.mp4/OjF765iVuF8.mp4 210 Exploring properties of matrix multiplication https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/v/identity-zero-matrix-equation 2021-03-19T16:21:23Z Using identity & zero matrices Sal solves a problem where he has to determine whether unknown matrices are zero or identity to make an equation true. Sal Khan video https://cdn.kastatic.org/googleusercontent/FzP8niHmJ1BTwMOKj9PPOlgR9kjWMSU145Cat24UQdteColUT7c_-jnpf1hYF9bwbQCdvygUcvOGT9Z1qLL_2E-zpg Using identity & zero matrices Sal solves a problem where he has to determine whether unknown matrices are zero or identity to make an equation true. https://cdn.kastatic.org/ka-youtube-converted/ikadoCpDNT8.mp4/ikadoCpDNT8.mp4 238 Exploring properties of matrix multiplication https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/a/intro-to-identity-matrices 2024-09-24T05:53:21.295694303Z Intro to identity matrices Learn what an identity matrix is and about its role in matrix multiplication. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/a/matrix-multiplication-dimensions 2024-09-24T05:53:21.295694303Z Matrix multiplication dimensions Learn about the conditions for matrix multiplication to be defined, and about the dimensions of the product of two matrices. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/a/properties-of-matrix-multiplication 2024-11-04T03:21:18.50878448Z Properties of matrix multiplication Learn about the properties of matrix multiplication (like the distributive property) and how they relate to real number multiplication. article