Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. 12x₁2 + 12x₂² + 12x3² + 12x4² +24x₁x₂ +24x3x4-32X1X4+32X₂X3 What is the most precise classification for the quadratic form? OA. Negative definite OB. Positive semidefinite OC. Negative semidefinite OD. Indefinite O E. Positive definite The new quadratic form is y Dy=0

Classify the quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. 2 2 8x₁² + 8x₂² +8x3² + 8x4² + 16x₁x2 + 16x3 x4 +30x₁x4-30x2x3 What is the most precise classification for the quadratic form? O A. Positive semidefinite OB. Negative semidefinite O C. Positive definite OD. Indefinite OE. Negative definite The new quadratic form is y' Dy=

Make a change of variable, x = Py, that transforms the quadratic form x? + 10xjx2 +x; into a quadratic form with no cross-product term. Give P and the new quadratic form.

Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. - 3x, + 6x1 x2 + 5x% Choose the most precise classification for the quadratic form. O A. Positive semidefinite O B. Negative semidefinite C. Indefinite O D. Negative definite O E. Positive definite The new quadratic form is y' Dy = (Simplify your answer.)

Classify the quadratic form. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P. x,? – 6x1x2 + x2²

Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one with no cross-product terms. Write the new quadratic form. -x; - 3x - 5x3 - 5x - 2x, x2 + 2x,x3 + 2x,×4 + 4x3×4 Classify the given quadratic form. O A. Negative definite B. Indefinite C. Positive semidefinite 'D. Negative semidefinite O E. Positive definite The new quadratic form is y' Dy = (Simplify your answer.)

Classify the quadratic form. Then make a change of variable, x Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P. Q8. x?- 4x,x2 + 4x,?

Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. 2 2 6x₁ + 6x₂ 2 + 6x3 + 12x1x2 + 12x3x4 + 16x₁x4-16x2x3 + 6x4 What is the most precise classification for the quadratic form? O A. Positive semidefinite B. Indefinite OC. Positive definite OD. Negative semidefinite OE. Negative definite The new quadratic form is y' Dy =

Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. 2 2 8x₁ +8x2 + +8x3² +8X4 2 2 + 16x₁x2 + 16×3×4 - 30x₁x4 +30x₂x3 What is the most precise classification for the quadratic form? A. Indefinite B. Negative semidefinite C. Positive definite D. Negative definite E. Positive semidefinite T The new quadratic form is y' Dy= 2 9y1 2-25y3 2-2514 +9y₂ 2

Classify the quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. 2 4x1 2 2 +4x2 +4x3 2 +4x4 + 8x₁x₂ + 8×3×4 + 6×₁X4 − 6x2x3 What is the most precise classification for the quadratic form? A. Positive definite B. Negative definite C. Indefinite D. Positive semidefinite OE. Negative semidefinite Т The new quadratic form is y Dy =