Let x and y be real numbers and consider the column vectors u=left[begin{array}{c}2 x -3end{array}right] and v=left[begin{array}{c}3 -4 -yend{array}right] If the inner product of u and v is -5 , then what is 3 y-4 x ?

Question

Let x and y be real numbers and consider the column vectors u=left[begin{array}{c}2  x  -3end{array}right] and v=left[begin{array}{c}3  -4  -yend{array}right] If the inner product of u and v is -5 , then what is 3 y-4 x ?

Accepted Answer

Step:1 ：Find the inner product of u and v: (2*3 + x*(-4) + (-3)*(-y) = -5)Step:2 ：Solve for x in terms of y: (x = frac{3y}{4} + frac{11}{4})Step:3 ：Substitute x into the expression (3y - 4x) and simplify: (3y - 4left(frac{3y}{4} + frac{11}{4}right) = -11)Step:4 ：boxed{-11}

Answer

Step: 1 ：Find the inner product of u and v: (2*3 + x*(-4) + (-3)*(-y) = -5)Step: 2 ：Solve for x in terms of y: (x = frac{3y}{4} + frac{11}{4})Step: 3 ：Substitute x into the expression (3y - 4x) and simplify: (3y - 4left(frac{3y}{4} + frac{11}{4}right) = -11)Step: 4 ：boxed{-11}

Let $x$ and $y$ be real numbers and consider the column vectors $u=\left[\begin{array}{c}2 \\ x \\ -3\end{array}\right]$ and $v=\left[\begin{array}{c}3 \\ -4 \\ -y\end{array}\right]$ If the inner product of $u$ and $v$ is -5 , then what is $3 y-4 x$ ?

Answer

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