Calculate:  a) AB b) A’D’B’ c) Find the determinant of D. Show all work

Q: Prove the identity without evaluating the determinant (Using properties). a1 b1+ tai ci+rb1 + sa1|…

A: Use the below properties of the determinant. 1) The determinant remains unaltered if its rows are…

Q: In Exercises, use determinants to find out if the matrix is invertible. 3 2

A: Consider the provided matrix, Find out the determinant of the given matrix,

Q: A = n N5 - -Om cO 3O17

A: We have to find out the determinant of A by using Laplace's theorem. The given matrix A is…

Q: 2. Use row/column operations and properties of determinants to show that (Do not expand using…

A:

Q: Using the theorem on determinants, show that |1 а a? b b2 = (b – a)(c – a)(c – b) c2 A = 1 %3D

A:

Q: Use the determinant version of the cross product to compute u X v.

A: The given vectors are u=011, and  v=3-12 The objective is to find the cross product of the vectors u…

Q: Compute the determinants in Exercises using cofactor expansion alongany row or column that seems…

A: Given matrix: A=0a0bcd0e0   For any n×n matrix A, determinant using cofactor expansion on the first…

Q: Find a 2 * 2 determinant formula for the area of the triangle in the xy-plane with vertices at (0,…

A: Given, vertices of the triangle are

Q: Show that y = e", y = e2" , y = x and y = x² are linearly indepent functions %3D Hint: Use the…

A: To show y=ex,y=e2x,y=x,y=x2 are linearly independenr we are going to provethat the workian is…

Q: Using the theorem on determinants, show that |1 a2 a A 1 (ь — а) (с — а)(с — b) b b2 | - c²

A:

Q: Compute the determinants in Exercises using cofactor expansion alongany row or column that seems…

A: The given matrix is 0a0bcd0e0

Q: 3 а 2 b P = R = where a, b e R. (a) Find a, b, c, d e R such that RP (b) For u E R, let A = -2 and…

A: The inverse of a matrix is given by the expression: Here, A is any square matrix. When the…

Q: Let a,b,c be three numbers such that a+b+c+d30. Find the determinant of the following matrix. b+c…

A:

Q: 2а 2b b - c 2b 2а а+c| %3D-2(а — b)?(а + b) а +b a+ b а

A: This is a determinant problem

Q: Consider four row vectors u, u, w, z of size 1 x n each and let a, bER Then. by multilinearity of…

A: The given statement is

Q: Use expansion by cofactors to find the determinant of the matri: 4 20 0 6 0 1 2 4 5 0 0 35 4 0 0 6 3…

A:

Q: Compute the determinants in Exercises using cofactor expansion alongany row or column that seems…

A: We have to compute the determinant using cofactor expansion along any row: ab00aba0b We know that if…

Q: Find the determinant in a) and b) where га CT f il det d e 7 %3D Lg_h а b C а C] а) А- 15g d f 5h…

A: Following are some results concerning determinant of a matrix. If we interchange any two rows, then…

Q: Using the theorem on determinants, show that a² |1 A = а b b2 (b – a)(c – a)(c – b) 1 c2

A:

Q: Prove the identity without evaluating the determinant (Using properties). ai b1 + tai c1+ rb1 + sa1…

A: Note the following properties of determinant : Property 1 : If any two rows (or columns) of any…

Q: Find the vector, not with determinants, but by using properties of cross products. (i x j) x k

A:

Q: sin'a cos'a cos²x sin?x 1 1 10 12 2

A: We use properties of determinant

Q: Prove the identity without evaluating the determinant (Using properties). a1 bi + tai ci+rb1 + sa1…

A: We have to prove the identity…

Q: Use the determinant version of the cross product to compute u X v.

A: Given vectors: u=3-12,  v=011

Q: c. Given that the vector à = a,î + azĵ + azk and b = b,î + b2ĵ + bzk. Show that the vector product…

A: Given:     a→=a1i+a2j+a3k     b→=b1i+b2j+b3k  The vector product of two vectors  a→=a1i+a2j+a3k and…

Q: Use the determinant version of the cross product to compute u X v.

A: Solution: Consider the two vectors a = a1i + a2j + a3k and b = b1i + b2j + b3k and their cross…

Q: In Exercises, use determinants to find out if the matrix is invertible. 1 -1 [5 -3 -2 3.

A:

Q: Let a,b,c be three numbers such that a+b+c+d=0. Find the determinant of the following matrix. ++c…

A:

Q: la C a b a

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

Q: Prove the identity without evaluating the determinant (Using properties). a1 b1+ tai c1 + rb1 + sa1…

A: Let,  A=a1a2a3b1b2b3c1c2c3 Now, det A=a1a2a3b1b2b3c1c2c3         ~a1b1c1a2b2c2a3b3c3  (because the…

Q: 2. Use row/column operations and properties of determinants to show that (Do not expand using…

A:

Q: Using the theorem on determinants, show that 11 а а- А %3D |1 b b2| %3D (b — а)(с — а)(с - b) с с2

A:

Q: For the matric A find - The Determinant A (|A|). The Co-factor matric of A (Acof). - Where [-4 291…

A:

Q: Using the properties of determinants, prove that : 1 1 1 = (a – b)(b - c)(c - a)(a + b + c) a' b' c'

A: The solution to the given question is explained below.

Q: Prove the identity without evaluating the determinant (Using properties). a1 b1 + tai c1+rb1 + sa1…

A: Consider the LHS=a1b1+ta1c1+rb1+sa1a2b2+ta2c2+rb2+sa2a3b3+ta3c3+rb3+sa3. Use the sum property of…

Q: Compute the determinants in Exercises using cofactor expansion alongany row or column that seems…

A: We can find the value of the determinant by using Cofactor expansion. For n×n matrix We have the…

Q: Use the concept of volume to explain why the determinant of a 3x3 matrix A is zero if and only if A…

A:

Q: Evaluate the determinants to verify the equation.

A:

Q: Use the theorem for three linearly independent vectors (that is, calculate a determinant) to…

A: Here it is given that u ,v ,w  Find it is u, v, and w are linearly dependent or independent.

Q: Find the determinants in Exercise , assuming that

A: Determinant is used to solve linear equations. To find the inverse of a matrix determinant is used.…

Q: Express the determant expression of a 3 X 3 matrix using cofactor and minor, Using this, try to…

A:

Q: Find the volume of the parellepiped spanned by the three given vectors à, v and w (hint: use a…

A: The volume will be u.(v×w), the cross product will br applied be the determinant.

Q: Let B={V₁ =,2 =, V3 =}. Use determinant to determine whether B is linearly independent or linearly…

A:

Q: Given that the vector å = a,î + a2j + azk and b = b,î + b2j + b3k. Show that the vector product of å…

A:

Q: a +d b+e c+, Find the determinants in Exercises, where d

A:

Q: For the matric A find - The Determinant A (|A|). The Co-factor matric of A (Acof). Where T-4 2 -9]…

A: Given :A=-42-93411-32

Q: inition of determinant of T, prove that det(T-¹) = (det(T))−¹ (Hir erminant of the identity man?)

A:

Q: Use a determinant to find an equation of the plane passing through the points.(0, 0, 0), (1, 0, 3),…

A: Consider the following points: 0,0,0, 1,0,3, 0,3,4 x1=0,y1=0,z1=0x2=1,y2=0,z2=3x3=0,y3=3,z3=4

Q: Let A= (aj) and B = (b;) be the square matrices of order 3 such that bj = 3i+j aj for 1si,j< 3. If…

A: The given question can be solved as shown in step2.

Q: Find the determinants in Exercise , assuming that

A: