please send handwritten solution for Q 1 1. Is the following set of vectors in R³ linearly dependent:{(1,0,3), (2, 1, –2), (0, – 1, 8), (7, 2, 3)}?Give the dimension of the subspace spanned by the vectors.2. Determine all real numbers x € R for which the vectors (x, 0, 1), (2, x, 3), and (4, 5, 6) arelinearly independent.3. Find the set of vectors in R³ which are orthogonal to both (4, 2,0) and (3, 6, 9).4. Use properties of matrix algebra (Notes 8) to help evaluate the following:-2[o 3(a)7(b)5. Use a sequence of elementary row operations to calculate the inverse of the followingmatrix:ГО 1 01A =12 32 016. Using the previous result, solve the system of equations2x + z = 2y = 8x + 2y + 3z = 4

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Answered: 1. Is the following set of vectors in…

1. Is the following set of vectors in R³ linearly dependent: {(1,0,3), (2, 1, –2), (0, – 1,8), (7,2, 3)}? Give the dimension of the subspace spanned by the vectors.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...

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Question

please send handwritten solution for Q 1

1. Is the following set of vectors in R³ linearly dependent:
{(1,0,3), (2, 1, –2), (0, – 1, 8), (7, 2, 3)}?
Give the dimension of the subspace spanned by the vectors.
2. Determine all real numbers x € R for which the vectors (x, 0, 1), (2, x, 3), and (4, 5, 6) are
linearly independent.
3. Find the set of vectors in R³ which are orthogonal to both (4, 2,0) and (3, 6, 9).
4. Use properties of matrix algebra (Notes 8) to help evaluate the following:
-2
[o 3
(a)
7
(b)
5. Use a sequence of elementary row operations to calculate the inverse of the following
matrix:
ГО 1 01
A =
1
2 3
2 0
1
6. Using the previous result, solve the system of equations
2x + z = 2
y = 8
x + 2y + 3z = 4

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