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 of a, b and c so that p(A) = O is the zero matrix.

Q: Determine if the columns of the matrix A = - 2 1 4 0 84 4 t 0 are linearly independent.

A: Here we need to show that columns of matrix A are linearly dependent or independent.We all know that…

Q: Find the matrix of the quadratic form. Assume x is in R°. 5x - 4x3 + 3x3 + 18x,x2 - 4x,×3 b. 3x -…

A: We want to find matrix of given quadratic form.

Q: Find the matrix of the quadratic form 2x,² + 3x2² – x3² – 4x1x2 +2 x1X3 + 6x2X3

A: The symmetric matrix for quadratic form ax12+bx22+cx32+dx1x2+ex2x3+fx1x3 can be written as…

Q: Find the matrix of the quadratic form. Assume x is in R?. a. 3x - 8x,x2 + 2x3 b. 5x, + 18x,x2

A:

Q: Let A =  -2 1     0 3     and    B =  2 -3     1 −2. Find a matrix X satisfying the matrix…

A: The given matrices, A=-2103 and B=2-31-2 We have to find the matrix X, that satisfies 2A+X=3B

Q: Find the matrix of the quadratic form associated with the quadratic equation 3x2 − 16xy + 3y2 − 13 =…

A: The given quadratic equation is 3x2-16xy+3y2-13=0. We have to find a matrix.

Q: Perform the following operation: 1- -5 4 3] a +a 3 1 4 -a ||

A: Given that we have to the find the product of given matrix

Q: Consider the matrix A = A. Verify that the matrix B: = I. 2 1 = = B. Use this fact to solve the…

A: AA-1= A-1A = I; where 'I' is the identity matrix.

Q: the matrIX A into a product QDQ" where Q is orthogonal and D is diagonal.

A: Given,          A=-5-1-1-1-3-1-1-1-3

Q: Let V = [- 7, – 7,0] and V½ = [0, 3, – 4]. Use the Gram- | Schmidt procedure to construct an ordered…

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Q: Find the range of a (2 × 3) matrix B with rank(B) = 2

A:

Q: Write 2x + 3y + z + 5t = 8 as a matrix A (how many rows?) multiplying the column vector x = (x, y,…

A: Given: Equation is Objective:Represent the equation in matrix form, , where  is the coefficient…

Q: Given A = 1 0 0 -3 1 1 1 - 2 -1 " x = and b = 300 150 400

A: Given that the system Ax=bHere A=1-3101-201-1 , b=300150400

Q: a. Construct a 3 × 2 matrix A such that Aỡ = ♂ has only the trivial solution. A = = b. Construct a 3…

A: To Do: (a) Construct a 3×2 matrix A such that Ax→=0→ has only the trivial solution. (b) Construct a…

Q: Solve for the 2 x 2 matrix X: X + 2 23 5 3 X.

A: Introduction: A-1 stands for Inverse of Matrix for matrix A. There is a straightforward formula for…