Find the vector x determined by the given coordinate vector [x]g an 4. B= 3 - 1 [x]B %3D -5 -5 -2 (Simplify your answers.)

Q: -5 and 4 4 k are orthogonal. k =

A: We know that if two vectors u & v are orthogonal to each other then the dot product or scalar of…

Q: Find the vector x determined by the given coordinate vector (x)g and the given basis B. -2 - [x]g =…

A: A set B is said to be basis of any vector space if (1) it is linearly independent set. (2)B spans…

Q: Find the coordinate vector |x relative to the given base B={b, ,b2} -3 5

A: To the coordinate vector xβ=x1x2 such that…

Q: Let a and b be two unit vectors what is: 1) аx (a-b) 2) (аxb) + (bxа) 3) а-(a+ (а х b)) 4) а- (ахb)…

A: We have to solve given problem:

Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. - 1 2 5 - 8…

A: Find the vector x determined by the given coordinate vector [x], and the given basis B.

Q: reflect a vector over the y-axis, stretch it horizontally by a factor of 6, and stretch it ve by a…

A: Topic:- matrix algebra

Q: Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. - 4 - 4…

A:

Q: snip

A:

Q: b) Find values of h for which the vectors are linearly dependent. Justify your answer. 5

A:

Q: Q2: Find the vector and unit vector (u) in the direction of the vector P2 = (-3,0, 6) to P, = (4, 6,…

A: Let us consider the vector P=(a,b,c) and Q=x,y,z. The vector in the direction of P to Q is obtained…

Q: Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation a = x+ (x.y)y. a)…

A: Solutions

Q: Suppose you know that f:R? → R³ is a linear function, and that (1)- 5 and 2 (a) (6 points) What is ƒ…

A:

Q: Use the figure to find the specified vector. Find -a. .. -10-8 -6 t2 4 x0T. 8.9 ...

A: We have to find -a.

Q: Find the coordinate vector [x]g of x relative to the given basis B = {b1, b2, b3}. -2 9 b, = b2 3 b3…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Which of the following is a vector equation of the equation below: 꼭 3D y-1 Ox = -2 -7t y = 1 + 3t O…

A: Given equation of line is: x+2-7=y-13

Q: Find the coordinate vector [x]R of x relative to the given basis B= {b1. b}. 2 1 b2 = - 4 %3D [X]g…

A:

Q: Find a and ß that solve the vector equation: -(1) - •(;) - ) 26 28

A: The given problem is to find the values of the unknown variables that can solve the given vector…

Q: Find the point functions t= d6i +(e-6); +(-€)4 and 40=(2+2-/it (5- €);t (1-56)4 Intersect. at which…

A: Given: Two vector functions as r1t=2ti+t2-6j+-13t3k and r2t=2+2ti+5-tj+1-5tk, To find: The…

Q: Find values of h for which the vectors are linearly dependent. Justify your answer.

A:

Q: 2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. and HNO 8…

A: We use definition of linearly independent vectors.

Q: Find values of h for which the vectors are linearly dependent. Justify your answer. 3 7.

A: Let v1=1-14, v2=3-57, v3=-15h

Q: Let -16 -4' V1 16 and w = 43 Is wa linear combination of V1 and V2? Fill in the coefficients of the…

A: Given that:v1=4-5-1, v2=-16163, w=-44438

Q: Find the equation of the following lines in the form specified in bold. a) A vector equation of a…

A: As per our guidelines we are supposed to answer only one question i.e. question no (a). For the…

Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. 4 4. -3 B=…

A:

Q: Find the component form of the given vector. v = y 51 4 X -6 5 -4 2.

A:

Q: simplify the given vector expression. 2(a - 3b) + 3(2b +a)

A: The given vector expression is

Q: 3 -9- 2 : Suppose that vị = 7 V2 = V3 = -3 ,where h is some real number. Consider the following: -3…

A:

Q: Find the Value of h f00 which the vectors are linearly dependent 1. 3. 6. -3 1.

A: In the given question we have to find the value of h for which the given three vectors are linearly…

Q: Q6:- A/ Show that the vectors A. (BxC) B.(CxÃ)=C.(AxB), if the vectors A= 31-j+2k B=21+j-k C= i-…

A:

Q: Find the coordinate vector [x] of x relative to the given basis B = - 1 2 -⠀⠀⠀ b₂ 2 b3 -2 , X = - 3…

A:

Q: Consider three vectors A 6) (a) Find A (B+C). Fnl A C) Find A (8C) i Find Bx(A-C)

A: Here we have  A=4i+6j-2kB=2i+7j-kC=0i+3j+5k i) find A·(B+C) ii) find A·(B×C) iii) find A×(B+C)

Q: Express the vector t as a linear combination of the vectors u, v, and w. 0. -2 t3D -5 W = 24 1 t= u+…

A: By Compearing the entries i have solves the problem

Q: Find the vector x determined by the given coordinate vector [x]R and the given basis B. - 1 2 - 4 B=…

A: The vector x is the linear combination of the vector in basis B.

Q: The direction vector of the equation below is : c=−2+3t y = 3+2t O [3, -2] O [3, 2] O [2, 3] O 1-2,…

A:

Q: Find the coordinate vector [x]B of x relative to the given basis B= {b1, b2, b3}. 1 - 3 - 8 - 1 b2 4…

A:

Q: In a standard Cartesian coordinate system a vector, R, has an x-component of + 5.0 m and a y-…

A: In a standard coordinate system a vector R has an x- component of +5.0 m and a y- component of -4.0…

Q: Find the component form of the resultant vector. f = (-5, 12) g = (9,6) Find: -4f + 10g

A: If f⇀ = x1,x2   and g⇀ = y1,y2 then f⇀ + g→ = x1+y1 , x2 + y2

Q: Find the vector form of the equation of the line that passes through the points (1,-3,2) and…

A:

Q: describe the span of the given vectors a)geometrically b)algebraically

A:

Q: Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. -4 2 - 4…

A: Vectors are Linearly Dependent so it (two vector) can be written as a linear combination of third…

Q: nd the coordinate vector [x], of x relative to the given basis B = {b,,b2.b3}. 1 3 2 b1 1 b2 = - 1…

A:

Q: Find the coordinate vector [x]g of x relative to the given basis B = (b¡ b2 b3}. -2 1 3 b2 = b3 6.…

A:

Q: Solve for the unknowns in the vector equation below. 6. 6. 4 3 - a 7 a = b = ||

A: To solve for the unknowns in the vevtor equation below.

Q: Find the coordinate vector [x]B of x relative to the given basis B= {b1, b2} b1 b2 - 3 %3D X = - 10…

A:

Q: For what values of h are the given vectors linearly dependent? -24

A:

Q: For which real values of A do the following vectors form a linearly dependent set in R³? vị %3D 1 V2…

A: since given vectors are linearly dependent.

Q: Find the unknown entries in the vector equation. 4 4 + 3 a 7 a = b =

A:

Q: For which real values of A do the following vectors form a linearly dependent set in R? »- (A-) 1,…

A:

Q: Q2: Find the vector and unit vector (u) in the direction of the vector P2 (-3,0,6) to P1 = (4, 6, –…

A: We have to find the vector and the unit vector(u) in the direction of the vector P2=(-3, 0, 6) to…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.