Exploring the solution set of Ax = b
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@prettygoodprep on Instagram: "Linear Algebra: When does AX=b have a solution? The answer: If and only if B is a linear combination of the columns of A! Geometrically, imagine vectors A1, A2, A3 in R3 space. Their span might form a plane. Any vector B on that plane has a solution to AX=b. If B is off the plane, no solution exists! In this video: ✅ Equivalent forms of matrix notation ✅ Geometric interpretation of span ✅ When solutions exist vs when they don’t ✅ Example using row reduction to chec
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@prettygoodprep on Instagram: "Linear Algebra: When does AX=b have a solution? The answer: If and only if B is a linear combination of the columns of A! Geometrically, imagine vectors A1, A2, A3 in R3 space. Their span might form a plane. Any vector B on that plane has a solution to AX=b. If B is off the plane, no solution exists! In this video: ✅ Equivalent forms of matrix notation ✅ Geometric interpretation of span ✅ When solutions exist vs when they don’t ✅ Example using row reduction to chec
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