9. -3 27 If A =|0 . 3 0, then show that A3 – 9A + 1013 = 4, where I3 and o -3 i. -1 are unit matrix and null matrix of order 3 respectively. If A = P 1, then show that ii. B = 15 [4] (i) (AB)-1 = B-1A-1 (ii) (AB)" = B" A" (ii) (3A – 2B)T = 3A" – 2BT (iii) det(AB) = det A· det B -

Q: [2 3 Let A = and B = Find the (1,2)-entry of matrix X |3 5 given that XA+X=B. -3

A:

Q: 2. Prove that: k(4+ mB) - kA+(km) B for any mx n matrices A and B, and scalars k and m. (You may not…

A: 2 We have to prove that kA+mB=kA+kmB Where, A and B are m×n matrices and k and m are the scalars.…

Q: If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n…

A:

Q: 1 3 14. For the vector b=b, to be in the row space of the matrix A= then 256 by . by-4bz +1 lb, = 0…

A:

Q: 0 5 Let A= 4. diagonalizable matrix( A-XDX), then X and D are: 1 Select one: a. -5 X= -5 0 4 0. b.…

A:

Q: 4. Assume the invertible matrix A satisfies 10 4 2 1 3 1 1 A 4 A -1 -1 A 6 1 -2 3 4 -3 Find the…

A:

Q: (4) For the zero-one matrices A = and B = calculate %3D 0 0 1 1 (а) АЛВ (Ъ) АоВ (с) ВОВ

A: 4) Note:  AΛB = [aijΛbij] =[aijbij] , known as meet of A and B, only possible if matrix have same…

Q: ) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s) for…

A:

Q: 6. Suppose  X + XB = C, where X, B, and C are square matrices of the same size. a.  Derive an…

A: We will see that (I+B) must be invertible for existence of X.

Q: -14] is a linear combination of the vectors 16 if and only if the matrix equation Az = b has a…

A: Solving

Q: e/ By three ways Show that B= %3D isorthogunal matrix

A:

Q: 3- -4 0 1 2 1 - Find the adjoint matrix adj(A). 0 -1 Let A = 3 1 -2 3 -1 -1 2 a) 1 b) -1 2 1 2 -1 0…

A:

Q: B = . and = If X is a matrix that Let A = satisfies: Al, = 2B – XC. Then X is %3D

A:

Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 – 2xy – 2xz –…

A: Step:-1 Given quadratic form is  Q=2x2 +2y2 +2z2 -2xy -2xz -2yz Q=xyz 2-1-1-12-1-1-12 xyzQ=XTAXHere,…

Q: 5) A matrix A is diagonal if A¡j = 0 for i + j. Entries on the diagonal are not required to be…

A:

Q: 4. Find the cofactor matrix for the matrix. 5 9 1 8 5 6 4

A:

Q: b) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s)…

A: Negative definite: A square matrix is said to be negative definite if all the eigenvalues of the…

Q: [2ß ß Find all the values of the parameter ß for which the matrix is 3 5B] Consider invertible.

A: The matrix is given as , A=2ββ35β find all values of β for which the matrix is invertible.

Q: Find 6×6 matrix a, that satisfies the stated condition. Make your answers as general as possible by…

A: Let the genral 6*6 matrix is given by…

Q: 4s – r – 5t - (2r + 5s + 3t) 4t – (4r + 4s) 5s – 3r + 3t with r, s and t real. Find a matrix A such…

A: Let's find.

Q: 8. For the column matrix v=(v₁) we have explain then: (VA); =Vkaki

A:

Q: of |4|. örthogonal matrix Q. B C Q6. If A = D where B,C,D,E are n by n matrices, find |4 when BD =…

A:

Q: 4s – r – 5t - (2r + 5s + 3t) - 4t – (4r + 4s) - 5s – 3r + 3t vith r, s andt real. Find a matrix A…

A: given W=4s-r-5t-2r+5s+3t4t-4r+4s5s-3r+3t with r,s,t ∈ℝ find a matrix A such that W=ColA

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

A:

Q: 2 4 8 Suppose that A = LDU = 039 , then the matrix U is 0 0 7 equal to: 2 00 0 3 0 0 0 7 1 2 4 0 1 3…

A: Given:Suppose A=LDU=248039007To find : Matrix U

Q: 2 3 4 Let vi = 1 V2 = -2 V3 = 5, and E u = V2 3 Determine if u is in Col E, the column space of E.…

A: We have to determine u is in Col.E, the column space of E.

Q: 8. Only one of the following matrices cannot be singular for any choice of real numbers a and ß a a…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 - 2xy- 2xz -…

A: The objective is to find the symmetric matrix and diagonal form of the quadratic form…

Q: DEMONSTRATE THAT A A-1= A-1A = I      FOR THE MATRIX BELOW     1 -1 2 2 -3 4 1 0 3

A: Given matrix A=1-122-34103 We have to  prove that AA-1=A-1A=I We know that A-1=AdjAA

Q: .2) x(n)= n2+10 LTI h(n) ho, hỗ y(n)=10 1- By using 2x2 square input matrix, find h, and hy 2- Find…

A:

Q: -42 -36 Let A= and let B = 33 15 Solve the matrix equation for X : 3X = 3A – B. %3D

A:

Q: 2 3 3 Let A and B 3 5 given that AX+X=B. Find the (1,2)-entry of matrix X -3

A: Matrix multiplication, for matrix A and B can only be done if the number of columns of A is equal to…

Q: 16- Find k for which the matrix below be Involutary matrix. 4 4 3 3 b) 3. -2, Leave blank *0 ఇ

A:

Q: [1 2 1] A = 2 0 2 l2 3 kl give matrix. [A| = 1 , k=?

A:

Q: Let A be 5x1 matrix. Knowing that Rank (A) = 2. Then Nullity(A) is equal to: O 2 ONone of these

A: The solution is given below in the next step:

Q: [13 5 matrisinin rankının 2 olabilmesi için c aşağıdakilerden hangisi olamaz? 26 c if the given…

A:

Q: 2 Be A, a square matrix i. Given that A holds = 44 + 5I . Prove that A is reversible, and express A-…

A:

Q: 2.2.8 Show that if a matrix is positive definite then it is invertible, and its inverse is also…

A:

Q: 3 b Find the value of b that make the matrix A singular. 3 5 b =

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: 6. To identify 3 x 3 matrix Abr fis positive definite if and only if cfr r> 0, r²- ab >0 and 4>0. O…

A:

Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

Q: Let A be 5x6 matrix. Knowing that Nullity (A) = 2. Then Rank(A) is equal to: * None of these O 2 O 1…

A: We will find the rank of A as following.

Q: I1,I2,I3 of th

A: Here we have;  11I1+4I2+3I3=-4-15I1+4I2+4I3=163I1+4I2+17I3=3 let;  AX=B  where  A=1143-15443417,…

Q: 1- the rank of the matrix A.

A:

Q: 2. Find a single matrix equal to [1 - i 1+0, where i = √-1 (imaginary unit).

A: To find the product of the given 3 matrices.

Q: Q1 Create an matrix as follows 1- Set up the matrix A with its elements in order, the first column…

A:

Q: Consider the 3 x 3 matrix 1 2 3 A = b а -1 2 3 where a, b and c are some unknown scalars. If…

A: We are given a matrix: A=123abc-123 we need to find a, b and c such that A13 =24, A12 =-19 and A33…

Q: solve for matrix Colfficients A. CCX=l,y=l-),2=0]] 3.CCx=1,y=1,2 =]] CCa--4),-(-1をこ0 CCX=3,y=3,=)…

A:

Q: 7 Let K = -1 2 8 0 2 6 3. Express matrix K in quadratic form. -9

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.