Prove the identity without evaluating the determinant (Using properties). a1 b1 + tai ci+rb1+ sa1 a2 b2+ taz c2+rb2 + sa2 = a3 b3 + taz c3 + rb3 + sa3 a1 a2 a3 b1 b2 b3 C1 c2 C3

Q: Use the determinant of A to determine whether A has an inverse. 3 4 11 2 5 10

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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: Using the property of determinants, prove that |1 bc a(b+c)| 1 1 ab c(a+ b)| 2) ca b(c +a)| = 0

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

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Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

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Q: Using the theorem on determinants, show that a a? b b2 1 |1 A = 1 (b – a)(c – a)(c – b) - C

A: We have to show that A=1aa21bb21cc2=(b-a)(c-a)(c-b) by using the theorem on determinants .

Q: Use a determinant to decide whether the matrix is singular or nonsingular.

A: We know that a matrix is singular if and only if the determinant of A is zero.

Q: Explain why the determinant of a square matrix A is the same as the determinant of the transpose of…

A: Explanation

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

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Q: Can Cramer's rule be used to solve this system of equations? 161 + 7x2 = -5 9æ1 + 4x2 - 6 Yes No If…

A: Cramer's rule can be used to solve a system of equations only if the determinant of corresponding…

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: 2. Let B = {v₁ =, √₂ =, V3 =, V4 =}. Use determinant to determine whether B is linearly independent…

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

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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: Use a determinant to decide whether the matrix is singular or nonsingular.

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Q: Use the arrow technique to evaluate the determinant. 2 0 0 det 2 -1 2 1 8 -2

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Q: 6

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Q: Evaluate the determinants to verify the equation.

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Q: Evaluate the determinant of the matrix A by inspection

A: I listed two methods to find 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 either elementary row or column operations, or cofactor expansion, to find the determinant by…

A: We shall find determinant using elementary row operation.

Q: Compute the determinant by cofactor expansion. At each step, choose a row or column that involves…

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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: Use a determinant to decide whether the matrix is singular or nonsingular. O singular O nonsingular

A: If the determinant of a matrix is zero then the matrix is singular. If the determinant of a matrix…

Q: Determine whether each statement is true or false. If a statement is true, give a reason or cite an…

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Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

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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

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Q: Evaluate the determinant A by any method, |1 3 6 2 1 0 2 |0 A = |3 2 3 0 2 9 5 1 0 10 0 8 6 0 1 2

A: Consider , A = 1310206223302951010086012 We need to find determinant of A. For that we will use ,…

Q: Express the determinant in the form ai + bj + ck for real numbers a, b, and c.

A: The given determinant is  ijk1-2321-4.

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: 3. Prove that |B| = -|A| and identify what property of determinants. -4 1 4 -1 Let A- and B =5 -1 2…

A: To be proved - |B|=-|A| To be mentioned - what property this behavior shows

Q: Express the determinant in the form ai + bj + ck for real numbers a, b, and c.

A: To express the determinant in the form of ai+bj+ck for real numbers a,b,c. ijk5-6-1301 Solution:…

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

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Q: Using the property of determinants, prove that |24 18 30| 1) 2 1 17 = 0 4 3

A: We need to prove that                         .

Q: By using the properties of determinant prove that a? |b² + c² b² a? c2 + a? b2 4a?b?c? c2 c2 a² + b²

A: By using the determinant property that is:…

Q: Use 2 methods in evaluating the determinant. 9 -6 -5| 1.) -1 7 2 4 6m8

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Q: Use the arrow technique to evaluate the determinant. 3 0 det 3 -1 [ 1 6. -3 i

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Q: Use the following definition. a11 a12 a11 a12 If A = then |A| = a11a22 - a12a21. %3D [ a21 a22 a21…

A: 122334-13=12-13-3423=-16-612

Q: Compute the determinant by cofactor expansion. At each step, choose a row or column that involves…

A: If the determinant of abcdefghi is calculated by the cofactor expansion  along the first row, then…

Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

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Q: By calculating AB and evaluating the determinants, verify that det AB = det A det B a12 b12 for the…

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Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

A: Given matrix is 210110-1-14014-1071. To find: Determinant of matrix.

Q: Express the determinant in the form ai + bj + ck for real numbers a, b, and c.

A: To: Express the determinant in the form ai + bj + ck for real numbers a, b, and c. ijk2-16-351

Q: Ja + b а а a + b — b? (За + b) а а %3D а а + bl а

A: Let…

Q: Compute the determinant by cofactor expansion. At each step, choose a row or column that involves…

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Q: Use induction to prove that the determinant of a diagonal matrix is the product of all the entries…

A: Consider a diagonal matrix An, An=a10⋯00a2⋯0⋮⋮00⋯an Let Pn is is determinant of diagonal matrix An…