Solved on Jan 29, 2024

Calculate the difference between vector $\boldsymbol{a}$ and 5 times vector $\boldsymbol{b}$ , and express the result as a column vector.

STEP 1

Assumptions
1. Vector $\boldsymbol{a}$ is given by $\left(\begin{array}{l} 9 \\ 8 \end{array}\right)$ .
2. Vector $\boldsymbol{b}$ is given by $\left(\begin{array}{c} -4 \\ 6 \end{array}\right)$ .
3. We are asked to calculate $\boldsymbol{a} - 5\boldsymbol{b}$ .

STEP 2

First, we need to multiply vector $\boldsymbol{b}$ by the scalar $5$ .
$5\boldsymbol{b} = 5\left(\begin{array}{c} -4 \\ 6 \end{array}\right)$

STEP 3

Now, perform the scalar multiplication.
$5\boldsymbol{b} = \left(\begin{array}{c} 5 \times -4 \\ 5 \times 6 \end{array}\right)$

STEP 4

Calculate the result of the scalar multiplication.
$5\boldsymbol{b} = \left(\begin{array}{c} -20 \\ 30 \end{array}\right)$

STEP 5

Now that we have $5\boldsymbol{b}$ , we can subtract it from vector $\boldsymbol{a}$ .
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{l} 9 \\ 8 \end{array}\right) - \left(\begin{array}{c} -20 \\ 30 \end{array}\right)$

STEP 6

Perform the vector subtraction by subtracting the corresponding elements.
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 9 - (-20) \\ 8 - 30 \end{array}\right)$

STEP 7

Calculate the result of the subtraction.
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 9 + 20 \\ 8 - 30 \end{array}\right)$

STEP 8

Simplify the resulting vector.
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 29 \\ -22 \end{array}\right)$
The answer as a column vector is $\left(\begin{array}{c} 29 \\ -22 \end{array}\right)$ .

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Calculate the difference between vector $\boldsymbol{a}$ and 5 times vector $\boldsymbol{b}$ , and express the result as a column vector.

STEP 1

Assumptions
1. Vector $\boldsymbol{a}$ is given by $\left(\begin{array}{l} 9 \\ 8 \end{array}\right)$ .
2. Vector $\boldsymbol{b}$ is given by $\left(\begin{array}{c} -4 \\ 6 \end{array}\right)$ .
3. We are asked to calculate $\boldsymbol{a} - 5\boldsymbol{b}$ .

STEP 2

First, we need to multiply vector $\boldsymbol{b}$ by the scalar $5$ .
$5\boldsymbol{b} = 5\left(\begin{array}{c} -4 \\ 6 \end{array}\right)$

STEP 3

Now, perform the scalar multiplication.
$5\boldsymbol{b} = \left(\begin{array}{c} 5 \times -4 \\ 5 \times 6 \end{array}\right)$

STEP 4

Calculate the result of the scalar multiplication.
$5\boldsymbol{b} = \left(\begin{array}{c} -20 \\ 30 \end{array}\right)$

STEP 5

Now that we have $5\boldsymbol{b}$ , we can subtract it from vector $\boldsymbol{a}$ .
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{l} 9 \\ 8 \end{array}\right) - \left(\begin{array}{c} -20 \\ 30 \end{array}\right)$

STEP 6

Perform the vector subtraction by subtracting the corresponding elements.
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 9 - (-20) \\ 8 - 30 \end{array}\right)$

STEP 7

Calculate the result of the subtraction.
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 9 + 20 \\ 8 - 30 \end{array}\right)$

STEP 8

Simplify the resulting vector.
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 29 \\ -22 \end{array}\right)$
The answer as a column vector is $\left(\begin{array}{c} 29 \\ -22 \end{array}\right)$ .

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Calculate the difference between vector a\boldsymbol{a}a and 5 times vector b\boldsymbol{b}b, and express the result as a column vector.

STEP 1

Assumptions1. Vector a\boldsymbol{a}a is given by (98)\left(\begin{array}{l} 9 \\ 8 \end{array}\right)(98​).2. Vector b\boldsymbol{b}b is given by (−46)\left(\begin{array}{c} -4 \\ 6 \end{array}\right)(−46​).3. We are asked to calculate a−5b\boldsymbol{a} - 5\boldsymbol{b}a−5b.

STEP 2

First, we need to multiply vector b\boldsymbol{b}b by the scalar 555.5b=5(−46)5\boldsymbol{b} = 5\left(\begin{array}{c} -4 \\ 6 \end{array}\right)5b=5(−46​)

STEP 3

Now, perform the scalar multiplication.5b=(5×−45×6)5\boldsymbol{b} = \left(\begin{array}{c} 5 \times -4 \\ 5 \times 6 \end{array}\right)5b=(5×−45×6​)

STEP 4

Calculate the result of the scalar multiplication.5b=(−2030)5\boldsymbol{b} = \left(\begin{array}{c} -20 \\ 30 \end{array}\right)5b=(−2030​)

STEP 5

Now that we have 5b5\boldsymbol{b}5b, we can subtract it from vector a\boldsymbol{a}a.a−5b=(98)−(−2030)\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{l} 9 \\ 8 \end{array}\right) - \left(\begin{array}{c} -20 \\ 30 \end{array}\right)a−5b=(98​)−(−2030​)

STEP 6

Perform the vector subtraction by subtracting the corresponding elements.a−5b=(9−(−20)8−30)\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 9 - (-20) \\ 8 - 30 \end{array}\right)a−5b=(9−(−20)8−30​)

STEP 7

Calculate the result of the subtraction.a−5b=(9+208−30)\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 9 + 20 \\ 8 - 30 \end{array}\right)a−5b=(9+208−30​)

STEP 8

Simplify the resulting vector.a−5b=(29−22)\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 29 \\ -22 \end{array}\right)a−5b=(29−22​)The answer as a column vector is (29−22)\left(\begin{array}{c} 29 \\ -22 \end{array}\right)(29−22​).

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Calculate the difference between vector $\boldsymbol{a}$ and 5 times vector $\boldsymbol{b}$ , and express the result as a column vector.

Assumptions
1. Vector $\boldsymbol{a}$ is given by $\left(\begin{array}{l} 9 \\ 8 \end{array}\right)$ .
2. Vector $\boldsymbol{b}$ is given by $\left(\begin{array}{c} -4 \\ 6 \end{array}\right)$ .
3. We are asked to calculate $\boldsymbol{a} - 5\boldsymbol{b}$ .

First, we need to multiply vector $\boldsymbol{b}$ by the scalar $5$ .
$5\boldsymbol{b} = 5\left(\begin{array}{c} -4 \\ 6 \end{array}\right)$

Now, perform the scalar multiplication.
$5\boldsymbol{b} = \left(\begin{array}{c} 5 \times -4 \\ 5 \times 6 \end{array}\right)$

Calculate the result of the scalar multiplication.
$5\boldsymbol{b} = \left(\begin{array}{c} -20 \\ 30 \end{array}\right)$

Now that we have $5\boldsymbol{b}$ , we can subtract it from vector $\boldsymbol{a}$ .
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{l} 9 \\ 8 \end{array}\right) - \left(\begin{array}{c} -20 \\ 30 \end{array}\right)$

Perform the vector subtraction by subtracting the corresponding elements.
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 9 - (-20) \\ 8 - 30 \end{array}\right)$

Calculate the result of the subtraction.
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 9 + 20 \\ 8 - 30 \end{array}\right)$

Simplify the resulting vector.
$\boldsymbol{a} - 5\boldsymbol{b} = \left(\begin{array}{c} 29 \\ -22 \end{array}\right)$
The answer as a column vector is $\left(\begin{array}{c} 29 \\ -22 \end{array}\right)$ .