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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §11.4 Matrices and Linear Equations, #37 · Linear Algebra · Linear systems

The equations … and … always have a nonzero solution

The equations $x + 2 y + 3 z$ and $4 x + 5 y + cz = 0$ always have a nonzero solution. The vector $u = (x, y, z)$ is required to be ______ to $v = (1, 2, 3)$ and $w = (4, 5, c)$ . So choose $u =$ ______.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.4 Matrices and Linear Equations, #37

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