1. Find scalars a,b,c that are real numbers such that at least one of a,b,c is non zero:
![at] +b]+cE]=R]](http://img.homeworklib.com/questions/efc33df0-f72d-11eb-8b32-17ab640863de.png?x-oss-process=image/resize,w_560)
2. Find a nonzero vector v in R^4 orthogonal to:
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1. Find scalars a,b,c that are real numbers such that at least
one of a,b,c is...
6. (a) Let V be a vector space over the scalars F, and let B =...
6. (a) Let V be a vector space over the scalars F, and let B = (01.62, ..., On) CV be a basis of V. For v € V, state the definition of the coordinate vector [v]s of v with respect to the basis B. [2 marks] (b) Let V = R$[x] = {ao + a11 + a222 + a3r | 20, 41, 42, 43 € R} the vector space of real polynomials of degree at most three. Write down...
Numbers 3,4,11 a. SublactiTlnb b. division of nonzero rationals c. function composition of polynomials with real...
Numbers 3,4,11
a. SublactiTlnb b. division of nonzero rationals c. function composition of polynomials with real coefficients d. multiplication of 2 × 2 matrices with integer entries e. exponentiation of integers 3. Which of the following binary operations are commutative? a. substraction of integers b. division of nonzero real numbers c. function composition of polynomials with real coefficients d. multiplication of 2 × 2 matrices with real entries e. exponentiation of integers 4. Which of the following sets are closed...
1- 2- 3- 1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for...
1-
2-
3-
1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
Please help and explain everything! thanks in advance Math 221 Review Linear Algebra II Review 1)...
Please help and explain everything! thanks in
advance
Math 221 Review Linear Algebra II Review 1) In Rº find three distinct non-zero vectors x,y,z which belong to the span of a = -18,-14, 26) B) In dimension of Rº find three distinct non-zero vectors x,y,z, no two of which are parallel to each other, and which belong to the span of a = (17.-5.-15)and b = (21, -3, -17) C) in R solve for a nonzero vector b in the...
Let S be the set/vector space of all real numbers of the form a sart(2)+ b'pi,...
Let S be the set/vector space of all real numbers of the form a sart(2)+ b'pi, where a, b are any real numbers, where we add these numbers the usual way, and multiply by real number scalars the usual way. Find, another, simpler way, of describing this vector space
thanks Consider the following matrices. Z= 2 . -1) (a) Find scalars a and b such...
thanks
Consider the following matrices. Z= 2 . -1) (a) Find scalars a and b such that Z = ax + by. (a, b) = (b) Do there exist scalars a and b such that W = ax + by? Yes Ο Νο (c) If ax + by + CW = 0, is it true that a = b = c = 0? Yes O No o. (d) Find scalarsa, b, and e, not all equal to zero, such that...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
3. Consider the following vectors, where k is some real number. H-11 Lol 1-1 a. For what values of k are the vectors linearly independent? b. For what values of k are the vectors linearly depende...
3. Consider the following vectors, where k is some real number. H-11 Lol 1-1 a. For what values of k are the vectors linearly independent? b. For what values of k are the vectors linearly dependent? c. What is the angle (in degrees) between u and v? 4. Here are two vectors in R". Let V = the span of {"v1r2} a. Find an orthogonal basis for V (the orthogonal complement of V). b. Find a vector that is neither...
only a-i T or F lit khd where it came from 4. You do not need to simplify results, unless otherwise stated. 1. (20pts.) Indicate whether each of the following questions is True or False by writin...
only a-i T or F
lit khd where it came from 4. You do not need to simplify results, unless otherwise stated. 1. (20pts.) Indicate whether each of the following questions is True or False by writing the words "True" or "False" No explanation is needed. (a) If S is a set of linearly independent vectors in R" then the set S is an orthogonal set (b) If the vector x is orthogonal to every vector in a subspace W...
Find the three angles of the triangle with the given vertices: P(1,1,1), Q(1,−5,2), and R(−2,2,6) Find...
Find the three angles of the triangle with the given vertices: P(1,1,1), Q(1,−5,2), and R(−2,2,6) Find a nonzero vector orthogonal to the plane through the points: A=(0,1,−1), B=(0,6,−5), C=(4,−3,−4)
6. (a) Let V be a vector space over the scalars F, and let B = (01.62, ..., On) CV be a basis of V. For v € V, state the definition of the coordinate vector [v]s of v with respect to the basis B. [2 marks] (b) Let V = R$[x] = {ao + a11 + a222 + a3r | 20, 41, 42, 43 € R} the vector space of real polynomials of degree at most three. Write down...
Numbers 3,4,11
a. SublactiTlnb b. division of nonzero rationals c. function composition of polynomials with real coefficients d. multiplication of 2 × 2 matrices with integer entries e. exponentiation of integers 3. Which of the following binary operations are commutative? a. substraction of integers b. division of nonzero real numbers c. function composition of polynomials with real coefficients d. multiplication of 2 × 2 matrices with real entries e. exponentiation of integers 4. Which of the following sets are closed...
1-
2-
3-
1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
Please help and explain everything! thanks in
advance
Math 221 Review Linear Algebra II Review 1) In Rº find three distinct non-zero vectors x,y,z which belong to the span of a = -18,-14, 26) B) In dimension of Rº find three distinct non-zero vectors x,y,z, no two of which are parallel to each other, and which belong to the span of a = (17.-5.-15)and b = (21, -3, -17) C) in R solve for a nonzero vector b in the...
Let S be the set/vector space of all real numbers of the form a sart(2)+ b'pi, where a, b are any real numbers, where we add these numbers the usual way, and multiply by real number scalars the usual way. Find, another, simpler way, of describing this vector space
thanks
Consider the following matrices. Z= 2 . -1) (a) Find scalars a and b such that Z = ax + by. (a, b) = (b) Do there exist scalars a and b such that W = ax + by? Yes Ο Νο (c) If ax + by + CW = 0, is it true that a = b = c = 0? Yes O No o. (d) Find scalarsa, b, and e, not all equal to zero, such that...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
3. Consider the following vectors, where k is some real number. H-11 Lol 1-1 a. For what values of k are the vectors linearly independent? b. For what values of k are the vectors linearly dependent? c. What is the angle (in degrees) between u and v? 4. Here are two vectors in R". Let V = the span of {"v1r2} a. Find an orthogonal basis for V (the orthogonal complement of V). b. Find a vector that is neither...
only a-i T or F
lit khd where it came from 4. You do not need to simplify results, unless otherwise stated. 1. (20pts.) Indicate whether each of the following questions is True or False by writing the words "True" or "False" No explanation is needed. (a) If S is a set of linearly independent vectors in R" then the set S is an orthogonal set (b) If the vector x is orthogonal to every vector in a subspace W...
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