Various advanced texts in linear algebra prove the following determinant criterion for rank: The rank of a matrix A is r if and only if A has some r × r submatrix with a nonzero determinant, and all square submatrices of larger size have determinant zero. (A submatrix of A is any matrix obtained by deleting rows or columns of A. The matrix A itself is also considered to be a submatrix of A.) Use this criterion to find the rank of the matrix. 1 6 5 30 -1| rank (A) =

Q: A culture of bacteria in a laboratory is subjected to a substance to decrease the number of bacteria…

A: Set e-t2+5t+3 equal to 100 and then solve for -t2+5t+3. e-t2+5t+3=100ln e-t2+5t+3=ln 100…

Q: discuss uniform continuity.

A:

Q: 2 Determine the general solution to the vector differential equation x' = Ax with A =0 -4 -3

A:

Q: d) Prove that the composition of two surjective linear transformations is again a surjective linear…

A: (d) Let T:X→Y be a surjective linear transformation and S:Y→Z also be the surjective linear…

Q: Inverse Laplace transform for e 2s is ... (s+3)2

A:

Q: . THe area enclased by the loop of the curved y= x (x - 3)° is Find the volume generated . revolved…

A: Here 1st we will find points where loop is formed and then shade the region bounded ,  To form the…

Q: [CLO-1] Use the he O Candida O Candidat O Candidat O Candidate

A: the given data is as follows   15 11 9 5 4   First A C D B C   Second B B C A D   Third  C…

Q: i. Show that 3 + 4i and 4-3i are associates in Z[i]. ii. Determine the splitting field of x4 + x2 +…

A: (i).

Q: At a corner gas station, the revenue R varies directly with the number g of gallons of gasoline…

A:

Q: test the convergehce and clivergence 2'coscnt)

A:

Q: In exercises 11–20, find (by hand) all critical numbers and use the First Derivative Test to…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Using the techniques described in section 2.6.4 of the Course Notes, find the global extrema of the…

A:

Q: 1 (a). 22 + 3 (b). (c). z2 – 2' 2 – 22

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…

Q: f (x) = cos(x). Consider Using the given f function at approximate by making use of f (x). the first…

A: The Taylor series of a real or complex-valued function f (x) that is infinitely differentiable at a…

Q: Write the multiplication table for the following commutative quotient ring: Z2[x]/(x³ + x² +x + 1).

A: Solution: The multiplication table below:

Q: Let X = (!,2) and T3} U = (1,2-)inel,2,U+ jult. %3D n+1 show that X is not T - space

A: This is a problem of Topology.

Q: Perform the Gram-Schmidt process on the following sequence of vectors. [27 [0] 4 3 4 6 -3

A:

Q: 3.1 If the Laplace transform of coswt is then find the Laplace Transform of the s2+w? following…

A:

Q: (1) Show that the series n+1 n-1 and n3 +1 n3 – 1 n=2 converge. Be very clear about the steps you…

A:

Q: Determine the null input answer of a described system by the equation: y[n] + 4y[n -2] = 2x[n]. The…

A:

Q: 4. Find the Inverse Laplace of 10 1 7 s+2 3s-5 s5

A:

Q: 1-2 Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates…

A: To fid the coordinates similar to a given polar coordinate we can use following formula…

Q: 5. Evaluate determinant D by: c. Chios Method 6 4 12 16 6 8 8 14 14 4 A = 4 6 16 12 2 2 10 18 10 14…

A:

Q: a) Use the Taylor theorem for function U(x, t) with the step size At. (x, is held constant) b)…

A:

Q: Given the following relations on the set of all integers where (x, y) e R if and only if the…

A:

Q: Problem 9.1. Harry consumes two lunches: salads and soup. The price of a salad is $12.50. Soup costs…

A: According to the given data, Harry consumes money on two lunches, salads and soups. The cost of…

Q: 1. The transport PDE, du has a family of solutions u = f(z – vt) where f can be any function. (a)…

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

Q: Solve by Laplace transform Utt - 9urr = 0, 00 %3D u(0, t) = u(T, t) = 0, u (x,0) = 0, u(x,0) = 2…

A: Use the given information.

Q: Give 5 sample problems for Orthogonal Trajectory (Application of Differential Equation). Provide…

A:

Q: test the Convergeh(e and n'coscnt)

A:

Q: a. The zero vector 0 is in ker(A) b. If x and y are in ker(A), then so is z = x + y. c. If x is in…

A:

Q: The following sales data are available for 2003- 2008: Year Sales 2003 33 2004 36 2005 38 2006 43…

A: 3-year moving average can be calculated by taking 3 data points from start and by calculating the…

Q: obtain the ualues of at x=0,1, o.2 using R.K method of fourth order Por the differential equalion…

A: (1) :- given differential Equation  y'=-y,  y(0) =1  We have to find value of y at 0.1 and 0.2  Take…

Q: Find Fourier series for the function f (x) = x\,- <x< T

A:

Q: 1- Show that the following subset is a subgroup. H = {0 e S, l0(n) = n}c S,

A: We have ,  H = σ ∈ Sn / σn = n  Here , H is subset of Sn Clearly , identity permutation is in  H.…

Q: One-way or two-way refers to the numbe of independent variables (IV's) in your Analysis c Variance…

A: In one way  , we have one independent variable.  While in two way we have two independent variables…

Q: NiHNZ Sub modute iffSNzo NZENI

A:

Q: Point A is 200 meters directly east of point B. The bearing from B to point C is S 50° E. If the…

A:

Q: HW. Solve the fallowihg firist order OsE

A:

Q: Find the first four nonzero terms of the Taylor series about 0 for the function…

A: To Find the first four nonzero terms of the Taylor series about 0 for the function f(x).

Q: 20 8. Compute the crossing number for each of the following graphs.

A:

Q: System of Nonlinear Equations Determine the solution of the simultaneous nonlinear equations using…

A: We will use the basic knowledge of numerical analysis to answer this question. Please note that…

Q: A thermometer reading 60° F is placed in an oven preheated to a constant temperature. Through a…

A: We will use Newtons law of heating to form differential equation '' temperature  of a body changes…

Q: P3 = {All functions of the form p(x) = ao + a1x + a2x² + a3x³}. Maybe you remember from calculus or…

A: Dimension of P will be infinity.

Q: The augmented matrix of a linear system has been reduced by row operations to the form shown.…

A:

Q: The period T of a pendulum is determined by T = 27 with L the length of the pendulum and g the…

A:

Q: Solve the linear programming problem a. Mrs. Reyes intense to make 500 boxes of chocolates with brar…

A: Introduction: The simplex method is a linear programming methodology for solving optimization…

Q: 21 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will…

A:

Q: Let f (x, y, z) = -13x² – y² + 5z². Calculate Vf (0, 6,7). (Write your solution using the form…

A:

Q: The area enclosed by the loop of the curve y^2=x(x-3)^2 is revolved about the x-axis. Find the…

A: Given the area enclosed by the loop of the curve y2 = x(x-3)2 is revolved about the x-axis. We have…