Let A = A basis for the image of A is 9 -6 6 9 Find a basis for the image of A (or, equivalently, for the linear transformation T(x) = Ax). -12 -10] -3 3 -3 3 -12 -10 .

Q: B. Let E = {e,, e2, e3} be the standard basis for R3 V, and T: R3 - V be a linear transformation wit…

A: Given: To explain the given statement as follows, To find the matrix for T relative to .

Q: --- A2 = A₁ = A3 = 3-[i].44 = [i]. A4 form a basis for the linear space V = R2X2. Write the matrix…

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Q: -1 -3 A 3 3 -7 2 3 -4. Find a basis for the image of A (or, equivalently, for the linear…

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Q: Let A = A basis for the kernel of A is 9 3 -12 - -9 -3 -3 -1 12 4 - Find a basis for the kernel of A…

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Q: A = A basis for the image of A is 6 -2 4 -3 -1 3 จ 1 −1 Find a basis for the image of A (or,…

A: Given A=64-2-4-31-2-1143-1

Q: Define T:R-→R² by T(x) = Ax. Find a basis B for R² with the property that [T]B is diagonal. - 3 - 3…

A: Given:T:ℝ2→ℝ2 is defined by Tx=AxWhere A=-3-3-1-5To find basis B for ℝ2 such that TB is diagonal.…

Q: Let p1,P2, P3 € P2 be defined by p1(t) = 2+t+t2, p2(t) = 2 – t+ 3t2, and p3(t) = 10+t+9t². Determine…

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Q: Let A = T -3 -8 8 -6 6 -6 -9-2 2 6 -6 6 Find a basis for the image of A (or, equivalently, for the…

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Q: A = A basis for the image of A is طانت سته -3 12 4 -1 1 -3 -2 -3 3 5 Find a basis for the image of A…

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Q: Let ) Let f: R² R² be the linear transformation defined by [f]] -2 4 >= [3³² $]* X. -5 f(x) = {(1,…

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 3x + 4x²} O s is linearly dependent. O…

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Q: Let A = A basis for the image of A is -1 −1 1 1 -6 -3 3 6 2 2 -2 -2 Find a basis for the image of A…

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Q: Let TR5 R³ be the linear transformation given by X1 x2 T x3 x4 X5 x1 + 2x2 x3 + 2x4x5 2x14x22x3 +…

A: ⎣⎢⎡​s+2t2s+5t2s​⎦⎥⎤​,s,t∈R⎣⎢⎢⎢⎢⎢⎡​x1​x2​x1​+2x2​+3x5​x5​x5​​⎦⎥⎥⎥⎥⎥⎤​,x1​,x2​,x5​∈R Nullity + Rank…