PLease help Question 211х —1-1 1 xa) Let A =1(i)Compute the value of det(A).(ii)For what values of x will the matrix be singular?b) Write down the quadratic form that corresponds to the following matrix.3.42 -1 -34 -3c) Examine whether the following quadratic forms are positive definite, negativedefinite or indefinite.(i)q(x) = 3x? + 2xy + 5yz + 7y2 – 2z?(ii)q(x) = 2x? – 4y² + 10xy – 7yz – 11xz + 3z?

Name: PLease help Question 211х —1-1 1 xa) Let A =1(i)Compute the value of d
Uploaded: 2024-03-20T07:07:37.000Z
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Description: PLease help Question 211х —1-1 1 xa) Let A =1(i)Compute the value of det(A).(ii)For what values of x will the matrix be singular?b) Write down the quadratic form that corresponds to the following matrix.3.42 -1 -34 -3c) Examine whether the following

Solution (a): A=x111x-1-11x, then (i). the determinant is…

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1 1 a) Let A = 1 x -1 -1 1 х (i) Compute the value of det(A). (ii) For what values of x will the matrix be singular? b) Write down the quadratic form that corresponds to the following matrix. (3 2 2 -1 -3 4 \4 -3 c) Examine whether the following quadratic forms are positive definite, negative definite or indefinite. (i) q(x) = 3x² + 2xy + 5yz + 7y² – 2z? (ii) q (x) %3D 2x? — 4у? + 10ху — 7уz — 11хz + 32?