Note that the first two columns of B are the same as those of A, while the third column of B is the sum of its first two columns. (a) Explain why Col(B) = Col(A). (b) Determine the rank of B. (c) Determine the rank of ATB.

Q: Let a = - 2ỉ - 4j – k and b = 4j + 2k. Find — ả + b. V

A:

Q: Find the values for c1, c2, and c3 to make sure that: c1 (10, 25, 1) + c2 (-15, 5, 0) + c3 (5, 0,…

A:

Q: Show that A×(BxC) + Bx(CxA) + Cx(AxB) =0.

A: We have to prove that LHS=RHS

Q: (-2y%3D 6. (2). (-8, )

A:

Q: (9y² + y - 7) + (7y² -y-4) = ]

A: We have to add 9y2+y-7+7y2-y-4

Q: 3 Let A= (MA-|| _23]~B-[2²] and = 6-9 -4 -6 Find - 2A + 2B. - 2A + 2B=

A:

Q: Ifv = [ -2, 4], compute and draw 2v, 1/2 v, and -2v.

A:

Q: Find (a) u × v, (b) v × u, and (c) v × v.…

A: Given : u =0,2,1v = 1,-3,4(a) u x v = ijk0211-34u x v =i 21-34    -j0114  +k021-3          = i(8+3)…

Q: 4x+2y=2 1.) 2x+2y=4

A: The given system of equation is: 4x+2y=22x+2y=4

Q: Let a = (-5, 5, 4) and 6 = (-1,-4, 5). (a) a × b x (41,-21,24) x (b) b × ā X = (c) (ã × b) × ã = (d)…

A:

Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: V(A - B) = A x (V x B) + B x (V x A) + (A - V)B + (B V)A,

A:

Q: Find the rank of A = ( 1   -1   2   3)                                       2  6  -8   1…

A: Rank of Matrix : It is the Number of Non Zero rows in reduced row echelon form.

Q: Let u = 4u + 5v (9, -2, -8) and v = (4, −3, −1).

A: The required solution is:<56,-23,-37>Explanation:

Q: 2. John invested P50,000.00 at an annual rate of 5% compounded yearly. Find the total amountin the…

A: Future value =PV(1+r)^t PV=50000 r=5%=0.05 t=15years

Q: Find å · b for å = (-2, ) and b = (-5, 12).

A:

Q: 11. (8-4w)(-6w+2)

A: To evaluate: 8-4w-6w+2 We know that x+px+m=x2+px+mx+pm

Q: Evaluate for r=(3,5) , s=(-6,4) , and t=(6,-1). 2r-(s+t)=

A: Recall the following facts.

Q: Find the values of c1, c2, and c3 so that c1 (4, –6, 2) + c2(-4, 3, 0) + c3 (-2,0, 0) = (-4, –3,…

A:

Q: 3. THREE 30' diameter and 20' deep DIMENSIONS: a. What is the volume of this cylinder (cell tower…

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Q: dx x²V(x² -4) Select one: a, 4x b. Vx? - 4) + C C. -Vx? -4) + C 2x d. Vx² - 4) 21 wwm + C 2x

A:

Q: If a = [1, 2]  and  b = [2, 7], find a + 2b.

A:

Q: Find a + b, 2a + 3b, lal, and la - b|. a = (4, –3), b = (-2, 5) a + b = (9,2) (2,9) 2a + 3b =

A:

Q: sinh e Incot3x h- dx St 1+9x²

A:

Q: Given w= (-4, 12), s=(-6, -2), and r=(4, 11), %3D find 6r-(w+s). 6r-(w+s) =(| , O)

A: This is related to vector addition sub, and mul

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Q: Find a × b if b = (–6, 9, —15) and à = (4, −6, 10) (-3,-2,0) (0,0,0) (1,-1,-1) (-24,-54,-150)

A:

Q: Find the value of a, b, and c if (a+b)(a+b+c)=21, (a+c)(a+b+c)=35, and (b+c)(a+b+c)=42.

A: First we need to make some equations and the we have to simplify them in order to get a, b and c.

Q: A rectangle with length / and width w has a diagonal of D inches. If the perimeter of the rectangle…

A:

Q: Find whether A and B are independent in the following cases : (AB) = 256 ; (aB) = 768 ; (AßB) = 48 ;…

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Q: show that (AB)-1 = B-1A-1

A: Given matrix A has a order of 2x2 while matrix B has a order of 2x3.

Q: A=-6 9. 2 4 3 -5

A:

Q: Find the inverse Laplace transform of the following functions. (s +1)e¬8 s2(s – 1) * a) F(s) = 5 b)…

A:

Q: 3.) (- 2y2-14v- 5)÷ (v+ 3)

A: Using algebraic operation

Q: = (-2, 11), s=(-1, -2), and r= (2, 10), find 3r-(w+s). 3r-(w+s) =(], D

A:

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (3, −2, 4), v = (1, 5, −3)

A:

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.