Questions: Refer to the vectors below. b=[3,4,-2] c=[-1,-4,3] d=[1,4,0] Compute the indicated vector. 2c-3b-d

Solution Steps

First, we need to multiply each component of vector \(\mathbf{c} = [-1, -4, 3]\) by 2:

\[ 2\mathbf{c} = 2 \times [-1, -4, 3] = [-2, -8, 6] \]

Next, we multiply each component of vector \(\mathbf{b} = [3, 4, -2]\) by 3:

\[ 3\mathbf{b} = 3 \times [3, 4, -2] = [9, 12, -6] \]

Now, we need to subtract the vectors \(3\mathbf{b}\) and \(\mathbf{d} = [1, 4, 0]\) from \(2\mathbf{c}\):

\[ 2\mathbf{c} - 3\mathbf{b} - \mathbf{d} = [-2, -8, 6] - [9, 12, -6] - [1, 4, 0] \]

Perform the subtraction component-wise:

\[ = [-2 - 9 - 1, -8 - 12 - 4, 6 - (-6) - 0] \]

\[ = [-12, -24, 12] \]

Final Answer