Q1: Answer by (True) or (false): 1) The transpose of a column matrix is a column matrix. 2 51 31 5| than A = -, 1 2) if A= |-1 3 and B = -2 41 1 2 1 -2 4] | 3) lim tan(2n).csc(4n) = - n-0 4 5 4) lim v4x² + 5x – 7 + 2x = 5) lim cos(x) = 1 x→, 2 6) logaxª = alogax = 1 %3D

Q: 5. x₁ + x₂ -3x1 3 +2x30 X₂ - 2x3 = 2

A: According to Bartley guidelines, these are separate questions. Please ask second question…

Q: Explain the fact “Cofactors are useful when matrices have many zeros”.

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Q: If B has a column of zeros, then so does BA if this product is defined. True O False 4

A: Given B has a column of zeros , then to find BA has a column of zero or not .

Q: Find the determinant of the following matrix (CLO7) ^= [41] Select one: O a. -3 O b. 5 C. -7 O d. 7

A: Given: Matrix:A=[2,5−1,1​​] Calculate the determinant for the matrix. Let`s assume a value for each…

Q: Give example 2. Determinant of a 5 × 5 matrix using properties of determinants

A: The solution of the problem is given in the next steps.

Q: Example: f=(f¹, f²): R³ → R² (-6) T1I2X3 that is, f¹(x) = x₁²² and ƒ²(x) = 1₁T2Tz. Then the Jacobi…

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Q: What are free columns?

A: A matrix is a rectangular array containing the set of numbers arranged in rows and columns. A matrix…

Q: By evaluating the determinants, verify the addition rule for the 2 x 2 case: a12 a22 la21 a22 la21…

A: Determinate

Q: [61] Diagonalize B = (by finding P and D) or explain why B isn't diagonalizable.

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Q: Let u = 3 II x₂ that satisfy the equation X2 -4 CHE 3 || -5 -3 (Simplify your answers.) and w= -4 -5…

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Q: Which 2x2 among the matrices/matrix below satisfy(ies) X^2 -5X + 21 = 0 where I and O are the 2x2…

A: We have to find the matrix that satisfies the given equation.

Q: 4. Express the following statements in one of the forms P V Q, P ^ Q, or ~ P. Be sure to clearly…

A: (a) Let P be the statement  P: The matrix A has zero determinant  Therefore , the given statement :…

Q: 6) Find the determinant: -2 3 4 3 4-2 5 6-3

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Q: a) Prove the following identity. (Do not use Examples.) (A+B+C)° = A" +B" +C" b) Is the product of…

A: Consider the given information. (a) Consider the left side of the equation. A+B+CT Simplify, the…

Q: Factor completely. qs - 8s + qf - 8f qs - 8s + qf - 8f =

A: We have to complete factor

Q: Please write clearly. Thank you

A: a) To find the matrix A corresponding to the quadratic form: We need to identify the coefficients of…

Q: Find the null space for A = 1 2 What is null(A)? {(} O A. O B. R? {} O C. span O D. span: 2 2. O E.…

A: We have to find the nulllspace of the given matrix .

Q: 1. Use row operations to find the inverse of '1 1 2 3 6 5 3 3 7

A: Solve for the inverse of the matrix

Q: 1 -[-3 3] 5 f A = of B. and AB = | -3-1 1 17 determine the first and second co

A: AB=-3-11117 B=1-3-35 We have to find A

Q: 4. Determine if the following sets are linearly independent or linearly dependent. Justify your…

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Q: 4. Explain what is wrong with the following "proof" that (ABC)" – C"B" A" for three conformable…

A: Properties of transpose of a matrix: (AB)⊥ = B⊥A⊥ Given: (ABC)⊥.

Q: Determine the conjugate of the product of, (3 – 2i) (4 + 3i)

A: solution:-3-2i4+3i=34+3i-2i4+3i=12+9i-8i-6i2putting i2=-1=12+9i-8i-6-12=12+9i-8i+6=18+i

Q: if (A|b) is in reduced row echelon form, prove that A is also in reduced row echelon form.

A: (A|b) is the augmented matrix formed by placing elements of matrix B to the right of elements of…

Q: 5) Given the function f(z) = 5+ 6z -4z2, find and simplify the difference quotient. f(z +h) – f(x)…

A: we have to find the difference quotient for the following function

Q: please continue matrices and find for x, y, and z cramers rule

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Q: ithout doing any row operations, explain in a short sentence why [137 0506 0028 0 10 A= 1 2 2 31 3…

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Q: in

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Q: 1. For the following quadratic forms (i) write down the symmetric matrix A (so the form is equal to…

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Q: 3. npor Find the dot product

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Q: 1. Let ƒ : R³ → R5 be the function given by f(x₁, x2, X3) = (x₁ + x2 − X3, 2x1 + 2x2 − X3, 3X1 + 3x2…

A: