https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:intro-to-matrix-inverses/v/inverse-matrices-and-matrix-equations 2022-10-07T00:22:18.752150461Z Inverse matrices and matrix equations In other videos, we've seen how matrices can represent systems of equations, and we've also seen how matrices whose determinant is zero don't have an inverse. In this video, we connect this two understanding, and by doing that way we understand how we can solve systems of equations with matrices. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/70d33dec-6fad-4ad4-932c-25db18e5d102_1280_720_base.png Inverse matrices and matrix equations In other videos, we've seen how matrices can represent systems of equations, and we've also seen how matrices whose determinant is zero don't have an inverse. In this video, we connect this two understanding, and by doing that way we understand how we can solve systems of equations with matrices. https://cdn.kastatic.org/ka-youtube-converted/a2S0kuXO3gE.mp4/a2S0kuXO3gE.mp4 450 Applications of determinants and matrices https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:representing-systems-with-matrices/e/writing-systems-of-equations-as-matrix-equations 2026-04-07T22:23:57.656416987Z Use matrices to represent systems of equations Systems of linear equations can be represented by a single matrix equation. Practice representing systems of 3 linear equations. Tomer Gal exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:solving-equations-with-inverse-matrices/v/solving-matrix-equation 2026-04-14T11:30:38.220334671Z Solving linear systems with matrices Sal solves that matrix equation using the inverse of the coefficient matrix. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZVdwCFDjELV4UUV_XhYa8zepybgZvK7-xXeL3eCatas1icovJmPH3HAue7UtG5pH_DZmn1sHjsCjrcOT3YYHJD7r Solving linear systems with matrices Sal solves that matrix equation using the inverse of the coefficient matrix. https://cdn.kastatic.org/ka-youtube-converted/0_DYEFtlCiM.mp4/0_DYEFtlCiM.mp4 400 Applications of determinants and matrices https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:determinants-ncert-new/x6f66cbee9a2f805b:applications-of-determinants-and-matrices/v/solving-system-of-3-equations-using-determinants 2025-05-22T13:12:03.767544849Z Solving system of 3 equations using determinants In this video, we bring together everything we've learnt in the chapters of Matrices and Determinants. We find the solution of a system of equations using the matrix method. We first check for consistency, then find the adjoint of matrix A before finding its inverse. We multiply inverse of A with B to find X. We get to this by premultiplying AX = B with the inverse of A. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Solving system of 3 equations using determinants In this video, we bring together everything we've learnt in the chapters of Matrices and Determinants. We find the solution of a system of equations using the matrix method. We first check for consistency, then find the adjoint of matrix A before finding its inverse. We multiply inverse of A with B to find X. We get to this by premultiplying AX = B with the inverse of A. https://cdn.kastatic.org/ka-youtube-converted/9_GjcZELhG0.mp4/9_GjcZELhG0.mp4 424 Applications of determinants and matrices https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:determinants-ncert-new/x6f66cbee9a2f805b:applications-of-determinants-and-matrices/e/solving-system-of-3-equations-using-determinants 2025-08-08T02:45:51.78671331Z Solving system of 3 equations using determinants Solving system of 3 equations using determinants Ashish Gupta exercise https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/v/word-problems-using-matrices-and-determinants 2025-05-22T13:12:03.767544849Z Word problems using matrices and determinants In this video, we solve word problems involving system of equations using the matrix method. We first represent 2 scenarios in the form of linear equations which we then use to write matrices. We then solve AX = B for the missing matrix X for both the scenarios. To do this, we first check for consistency, then find the adjoint of matrix A before finding its inverse. We multiply inverse of A with B to find X. We get to this by premultiplying AX = B with the inverse of A. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Word problems using matrices and determinants In this video, we solve word problems involving system of equations using the matrix method. We first represent 2 scenarios in the form of linear equations which we then use to write matrices. We then solve AX = B for the missing matrix X for both the scenarios. To do this, we first check for consistency, then find the adjoint of matrix A before finding its inverse. We multiply inverse of A with B to find X. We get to this by premultiplying AX = B with the inverse of A. https://cdn.kastatic.org/ka-youtube-converted/VZsQwNB-jG0.mp4/VZsQwNB-jG0.mp4 493 Applications of determinants and matrices https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:determinants/e/word-problems-using-matrices-and-determinants 2025-08-08T02:45:51.78671331Z Word problems using matrices and determinants Word problems using matrices and determinants Ashish Gupta exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:solving-equations-with-inverse-matrices/e/use-matrices-to-solve-systems-of-equations 2021-04-29T08:00:41Z Use matrices to solve systems of equations Practice solving systems of any number of linear equations using matrices and their inverses. exercise