Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 4 - (9x² + 3x), 7 − (16x² + 4x) and 55x² + 13x − 24. a. The dimension of the subspace His b. Is {4 (9x² +3x), 7 − (16x² + 4x),55x² + 13x − 24} a basis for P₂? choose c. A basis for the subspace H is { ✓ Be sure you can explain and justify your answer. }. Enter a polynomial or a comma separated list of polynomials, where you can enter xx in place of ².

Let W be the subspace of R4 defines as X1 X2 : x1 – 3x2 + 4x3 – x4}. - W = {x = X3 X4 Determine dim(W).

Let f be the invertible linear transformation represented by the matrix -2 ^-(-²¹) A = 1). 4 4 Find, in terms of and y, the equation of the image f(C) of the unit circle C. The equation is

Is the set of noninvertible 2 × 2 matrices a subspace of R2×2 ?

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Find an othonormal basis of the subspace that is the set of solutions to the following system:

Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 14x² − 17x + 10, 17x – 19x² – 11 and 9x² - 10x + 6. a. The dimension of the subspace H is b. Is {14x² - 17x + 10, 17x - 19x² – 11,9x² – 10x +6} a basis for P₂? choose c. A basis for the subspace H is { (where you can enter xx in place of x²) Be sure you can explain and justify your answer. }. Enter a polynomial or a comma separated list of polynomials

Find the dimension of the subspace Hof R2 spanned by

Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by −(4x2+5x+4), 1−(6x2+17x) and −(x2+2). The dimension of the subspace H is . Is {−(4x2+5x+4),1−(6x2+17x),−(x2+2)} a basis for P2? choose Be sure you can explain and justify your answer. A basis for the subspace H is { }. Enter a polynomial or a comma separated list of polynomials

State the Fundamental Subspace Theorem and give an example of its application in the case of a 2 x2 matrix.