By calculating AB and evaluating the determinants, verify that det AB = det A det B a12 b12 for the 2 x 2 case. Let A = and B a21 a22 b b2)

Q: 2. Find the determinant and invers a) -3 7 9 1 3 4 b) 1 9 3.

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Q: Jse determinant to calculate the area of a triangle with the following vertices: A = [2,1] B = [8,7]…

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Q: ) If G is a group and X is a G-set, then the subset (g in G: for all x

A: To explain the given statement is true or false as,

Q: Find the determinants in Exercise , assuming that

A: Given: abcdefghi=4

Q: a a. Evaluate: a a a b. Evaluate: 0 0 0 a a a al la a a a a a a c. Evaluate: 0 0 a a 0 0 0 a d.…

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Q: Using the theorem on determinants, show that 1 a a2 A = 1 b b2 = (b – a)(c – a)(c - b) 11 - с с2

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

A: Determinate

Q: Use the cofactor expansion to compute the following determinant: 5 6 5 det -3 9 7 %3D 6 9-8

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Q: Confirm the following identity without evaluating the determinant directly a₁ b₁+ta₁ c₁ +rb₁+sa₁ a2…

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Q: Find the determinant of the vector A = 2i+ 5j + 6k and B = 8k

A: determinant is nothing but finding the cross product. so, determinant of two vectors A and B = A×B

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: Let A be a 7 x 7 matrix. Write down the number of different expressions for the determinant of A we…

A: The minor matrix is the determinant of the matrix that is formed by deleting the ith row and jth…

Q: x + y – k = 0 -x – 2y + 7 = 0 4.x + 2ky – 20 = 0

A: Given system of equation is x+y−k=0−x−2y+7=04x−2ky−20=0........1 Equation 1 can be written as…

Q: Let-[:] and v-[³] u= v= Compute the area of the parallelogram determined by u, v, u + v, and 0, and…

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Q: Evaluate the determinant of the ナhc given mantrix using 91 92 93 result b2 bz = 5. C3

A: Given that:      a1a2a3b1b2b3c1c2c3=5

Q: Solve the problem below. Compute the value of x by determi 4 -1 2 3 2 X = 10 2 1 3 1 14 2 4 LO

A: We will use elementary row operation to find the determinant.

Q: A as the product of two determinants, show that A = 0. Hence, show that if ax² + 2hxy + by² + 2gx +…

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Q: Use determinants to find out if the matrix is invertible. - 25 2 - 5 -6 2 O 10 -3 1,

A: A metric is set to be invertible if its determinant is non zero. We will find the determinant of the…

Q: Find a 2 x 2 matrix such that 5 1 1 0 2 1

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Q: Use the appropriate property of determinants to find a. Do not evaluate the determinants. |0 3 -2 0…

A: 0  9 -61  0  111  2  0=a·0  3 -21  0  114  8  0

Q: 1 1 b+c a+c 1 -1 1 a+b+ 111 a b с 0-20 = 0

A: Aim:111b+ca+ca+b1-11+111abc0-20=0

Q: Calculate the determinant of 2x² + 3X + 5 O 23931 O 13249 O 12394 O 23419

A: