1. Decide whether each of the following statements is true or false. If true, explain briefly why, and if false, give an example where the statement fails. (a) (3 pts) If A is a 8 x 6 matrix and its null space has dimension 2, then the columns of A are linearly dependent. (b) (3 pts) If B is a 3 x 3 matrix and its characteristic polynomial is PB(A)=(A-4)(A-6)², then B is not diagonalizable. (c) (3 pts) If M and N are both 3×3 matrices and MN is invertible, then both M and N are invertible.

Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

Q: If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as…

A: It is given that, if a polynomial p(x) can be factored as a product of two lower degree polynomials…

Q: 21

A:

Q: What is a, if A = 2 4 is a singular matrix ? a Simplify (1+x)(1+x²)(1 – x + x?) in descending order…

A:

Q: [2 1 Q1 \a: find the inverse of the Matrix A= 1 1 2 1 -1

A: Given Matrix

Q: Some of the entries of the 3 x 3 matrix A are known as A -1 1 If det (A) = -–6 and A-1 find x.

A:

Q: Is the following statement correct or incorrect: The matrix notation of the quadratic form Q (xı,…

A: Solution : Given 2 variable quadratic form is                     Q(x1,x2)=5x12-10x1x2+x22 We have,…

Q: For A 3 1 N² = A. 2 find a 3 x 3 matrix X such that

A:

Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A:

Q: Which of the following matrices have characterestic polynomial p(A) = x2 - 10A +1 Select one: a. b.…

A:

Q: When reducing [A | I], a row in the A part consists of all zeros. What does this indicate about A-¹?…

A: We know that a matrix A is invertible if and only if A is non singular i.e. det(A)≠ 0

Q: This is a linear algebra problem pretaining to matrix. Please find the cofactor C11(A), C12(A),…

A:

Q: A. For any matrix A, give a simpler name for the matrix (At)t. B. Is it true or false that (2A)t =…

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Q: A=(41] [4] ( )= (-1) [₂] + (3) [₂] 2

A: Matrix multiplication is possible if we have two matrices A and B such that, order of A =m×n;order…

Q: For matrix A = (²3 §), if f(x) = X² - 2X, what is the answer to f(A)?

A:

Q: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: Select one:

A:

Q: Let A be a 3 x 3 matrix with det(A) = 0. Determine if each of the following statements is true or…

A: Since, you have posted a multiple parts question. But according to guidelines we will solve first…

Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A: Step 1: We'll perform row operations on A to reduce it to the identity matrix. Each row operation…

Q: Solve a b and c (brief answers only)

A: ### (a) If  A  is an  8×6  matrix and its null space has dimension 2, then the columns of  A  are…

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Q: If ri is a first row of a square matrix A and r3 is the third row of A such that ri = 2(r3) then |A|…

A: By applying elementry row operation we can find the value of |A|

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Q: Suppose A is an n x n matrix with A² = A. Show (I – 2A)−¹ = I — 2A.

A:

Q: For matrix A = A. C. (38 54 27 29. 29 27 54 38/ Select one: O A O B OC OD 4 (§). 3 if f(x) = X² - 5,…

A: A=4635f(X)=X2-5

Q: Given the matrix 2 1 A = |0 3 1 1 0 -1 and the polynomial p(x) = x³ + a.x² + bx + c, find the values…

A: GivenA=21003110-1p(x)=x3+ax2+bx+cp(A)=Op(A)=A3+aA2+bA+c=O21003110-1.21003110-1.21003110-1+a21003110-…

Q: Determine whether the following statement is true or false: If both matrices A of the size 2 × 2 and…

A: We have to state if the given statement is true or false.    According to our guidelines we can…