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Linear Algebra : Linear Algebra

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Example Questions

Example Question #135 : Matrices

$\begin{align*}&\text{Find the product }A\times B \\&\text{Where }A=\begin{bmatrix}18&-15&10&-15&-14&11\end{bmatrix}\text{ and }B=\begin{bmatrix}6\\-5\\-13\\9\\10\\-8\end{bmatrix}\end{align*}$

Possible Answers:

$\text{The multiplication cannot be performed.}$

Correct answer:

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since A has dimensions: }1\times6\\&\text{and B has dimensions: }6\times1\\&\text{The two vectors can be multiplied:}\\&\begin{bmatrix}18&-15&10&-15&-14&11\end{bmatrix}\times\begin{bmatrix}6\\-5\\-13\\9\\10\\-8\end{bmatrix}\\&(18)(6)+(-15)(-5)+(10)(-13)+(-15)(9)+(-14)(10)+(11)(-8)\\&-310\end{align*}$

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Example Question #136 : Matrices

$\begin{align*}&\text{Find the value of }C\text{ if }C=A\times B \\&\text{Where }A=\begin{bmatrix}16&-1&6&-20\end{bmatrix}\text{ and }B=\begin{bmatrix}10\\19\\-19\\1\end{bmatrix}\end{align*}$

Possible Answers:

$\text{The multiplication cannot be performed.}$

Correct answer:

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since A has dimensions: }1\times4\\&\text{and B has dimensions: }4\times1\\&\text{It is possible to find a value for }C:\\&C=\begin{bmatrix}16&-1&6&-20\end{bmatrix}\times\begin{bmatrix}10\\19\\-19\\1\end{bmatrix}\\&C=(16)(10)+(-1)(19)+(6)(-19)+(-20)(1)\\&C=7\end{align*}$

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Example Question #137 : Matrices

$\begin{align*}&\text{Find the product }A\times B \\&\text{Where }A=\begin{bmatrix}13&8\end{bmatrix}\text{ and }B=\begin{bmatrix}-12\\7\end{bmatrix}\end{align*}$

Possible Answers:

$\text{The multiplication cannot be performed.}$

Correct answer:

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since A has dimensions: }1\times2\\&\text{and B has dimensions: }2\times1\\&\text{The two vectors can be multiplied:}\\&\begin{bmatrix}13&8\end{bmatrix}\times\begin{bmatrix}-12\\7\end{bmatrix}\\&(13)(-12)+(8)(7)\\&-100\end{align*}$

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Example Question #138 : Matrices

$\begin{align*}&\text{Find the vector product }\\&\begin{bmatrix}-11&19&13&15&-18&6\end{bmatrix}\times\begin{bmatrix}3\\-14\\9\\-15\\-16\\10\end{bmatrix}\end{align*}$

Possible Answers:

$\text{The multiplication cannot be performed.}$

Correct answer:

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since our vectors have dimensions: }1\times6\text{ and }6\times1\\&\text{The two can be multiplied to find a product:}\\&\begin{bmatrix}-11&19&13&15&-18&6\end{bmatrix}\times\begin{bmatrix}3\\-14\\9\\-15\\-16\\10\end{bmatrix}\\&(-11)(3)+(19)(-14)+(13)(9)+(15)(-15)+(-18)(-16)+(6)(10)\\&-59\end{align*}$

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Example Question #139 : Matrices

$\begin{align*}&\text{Find the product }A\times B \\&\text{Where }A=\begin{bmatrix}13&-7&-14\end{bmatrix}\text{ and }B=\begin{bmatrix}-11\\12\\-4\end{bmatrix}\end{align*}$

Possible Answers:

$\text{The multiplication cannot be performed.}$

Correct answer:

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since A has dimensions: }1\times3\\&\text{and B has dimensions: }3\times1\\&\text{The two vectors can be multiplied:}\\&\begin{bmatrix}13&-7&-14\end{bmatrix}\times\begin{bmatrix}-11\\12\\-4\end{bmatrix}\\&(13)(-11)+(-7)(12)+(-14)(-4)\\&-171\end{align*}$

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Example Question #12 : Vector Vector Product

$\begin{align*}&\text{Find the value of }C\text{ if }C=A\times B \\&\text{Where }A=\begin{bmatrix}-5&5&-16&-19&8\end{bmatrix}\text{ and }B=\begin{bmatrix}18\\13\\-11\\-11\\-12\end{bmatrix}\end{align*}$

Possible Answers:

169

264

303

$\text{The multiplication cannot be performed.}$

Correct answer:

264

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since A has dimensions: }1\times5\\&\text{and B has dimensions: }5\times1\\&\text{It is possible to find a value for }C:\\&C=\begin{bmatrix}-5&5&-16&-19&8\end{bmatrix}\times\begin{bmatrix}18\\13\\-11\\-11\\-12\end{bmatrix}\\&C=(-5)(18)+(5)(13)+(-16)(-11)+(-19)(-11)+(8)(-12)\\&C=264\end{align*}$

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Example Question #11 : Vector Vector Product

$\begin{align*}&\text{Find the vector product }\\&\begin{bmatrix}-18&-4&-20\end{bmatrix}\times\begin{bmatrix}-9\\-11\\-11\end{bmatrix}\end{align*}$

Possible Answers:

426

$\text{The multiplication cannot be performed.}$

428

522

Correct answer:

426

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since our vectors have dimensions: }1\times3\text{ and }3\times1\\&\text{The two can be multiplied to find a product:}\\&\begin{bmatrix}-18&-4&-20\end{bmatrix}\times\begin{bmatrix}-9\\-11\\-11\end{bmatrix}\\&(-18)(-9)+(-4)(-11)+(-20)(-11)\\&426\end{align*}$

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Example Question #12 : Vector Vector Product

$\begin{align*}&\text{Find the vector product }\\&\begin{bmatrix}-8&-19&5&-9&2\end{bmatrix}\times\begin{bmatrix}-5\\-14\\0\\10\\12\end{bmatrix}\end{align*}$

Possible Answers:

192

311

240

$\text{The multiplication cannot be performed.}$

Correct answer:

240

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since our vectors have dimensions: }1\times5\text{ and }5\times1\\&\text{The two can be multiplied to find a product:}\\&\begin{bmatrix}-8&-19&5&-9&2\end{bmatrix}\times\begin{bmatrix}-5\\-14\\0\\10\\12\end{bmatrix}\\&(-8)(-5)+(-19)(-14)+(5)(0)+(-9)(10)+(2)(12)\\&240\end{align*}$

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Example Question #13 : Vector Vector Product

$\begin{align*}&\text{Find the vector product }\\&\begin{bmatrix}1&-7&8&9&-9\end{bmatrix}\times\begin{bmatrix}-20\\-8\\-7\\-2\\-20\end{bmatrix}\end{align*}$

Possible Answers:

$\text{The multiplication cannot be performed.}$

165

142

Correct answer:

142

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since our vectors have dimensions: }1\times5\text{ and }5\times1\\&\text{The two can be multiplied to find a product:}\\&\begin{bmatrix}1&-7&8&9&-9\end{bmatrix}\times\begin{bmatrix}-20\\-8\\-7\\-2\\-20\end{bmatrix}\\&(1)(-20)+(-7)(-8)+(8)(-7)+(9)(-2)+(-9)(-20)\\&142\end{align*}$

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Example Question #14 : Vector Vector Product

$\begin{align*}&\text{Find the vector product }\\&\begin{bmatrix}-3&-11&-9&-8&3\end{bmatrix}\times\begin{bmatrix}8\\-3\\4\\-20\\8\end{bmatrix}\end{align*}$

Possible Answers:

$\text{The multiplication cannot be performed.}$

193

157

Correct answer:

157

Explanation:

$\begin{align*}&\text{In order to multiply two vectors, }A\times b\text{, the respective dimensions of each}\\&\text{must be of the form }1\times n\text{ and }n\times 1\\&\text{Note that order does matter:}\\&(A\times b \neq b \times A)\\&\text{Since our vectors have dimensions: }1\times5\text{ and }5\times1\\&\text{The two can be multiplied to find a product:}\\&\begin{bmatrix}-3&-11&-9&-8&3\end{bmatrix}\times\begin{bmatrix}8\\-3\\4\\-20\\8\end{bmatrix}\\&(-3)(8)+(-11)(-3)+(-9)(4)+(-8)(-20)+(3)(8)\\&157\end{align*}$

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Linear Algebra : Linear Algebra

Study concepts, example questions & explanations for Linear Algebra

All Linear Algebra Resources

Example Questions

Example Question #135 : Matrices

Example Question #136 : Matrices

Example Question #137 : Matrices

Example Question #138 : Matrices

Example Question #139 : Matrices

Example Question #12 : Vector Vector Product

Example Question #11 : Vector Vector Product

Example Question #12 : Vector Vector Product

Example Question #13 : Vector Vector Product

Example Question #14 : Vector Vector Product

All Linear Algebra Resources

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