Find the values of x and y in the following scalar multiplication. {:[7*[[1],[x],[5]]=[[7],[-21],[y]]],[x=],[y=]:}

Question

Find the values of  x and  y in the following scalar multiplication.  {:[7*[[1],[x],[5]]=[[7],[-21],[y]]],[x=],[y=]:}

Bytelearn · Accepted Answer

Understanding scalar multiplication: Understand the scalar multiplication of a vector by a number. Scalar multiplication involves multiplying each component of the vector by the scalar (in this case, 7).Multiplying the first component: Multiply the first component of the vector by the scalar. 7 * 1 = 7 This matches the first component of the resulting vector, confirming that the scalar multiplication for this component is correct.Setting up the equation for the second component: Set up the equation for the second component of the vector after scalar multiplication. 7 * x = -21 Now we need to solve for x.Solving for x: Solve for x. x = -21 / 7 x = -3 This gives us the value of x in the scalar multiplication.Multiplying the third component: Multiply the third component of the vector by the scalar. 7 * 5 = 35 This should be the value of y in the resulting vector.Verifying the calculated values: Verify that the calculated values satisfy the original scalar multiplication equation. 7 * [1, x, 5] = [7, -21, y] Substitute x = -3 and y = 35 into the equation: 7 * [1, -3, 5] = [7, -21, 35] This matches the given resulting vector [7, -21, y].

Find the values of $x$ and $y$ in the following scalar multiplication. $\newline$ $\begin{array}{l} 7 \cdot\left[\begin{array}{l} 1 \\ x \\ 5 \end{array}\right]=\left[\begin{array}{c} 7 \\ -21 \\ y \end{array}\right] \\ x=\square \\ y=\square \end{array}$

Full solution

More problems from Powers of i

Related topics