What is the image point of \( (4,-6) \) after a translation right 5 units and up 4 units?

Bxercicio 1 Verifique se as funções abaixo saio transformaçôes lineares: a) \( F: \mathbb{R} \rightarrow \mathbb{R}^{2} \) dada por \( F(x)=(x, 2) \). b) \( F: M_{n \times n} \rightarrow M_{n \times n} \) dada por \( F(X)=P^{-1} X P \), onde \( P_{2 \times 2} \) é uma matriz invertivel fixada. c) \( F: \mathbb{R}^{4} \rightarrow \mathbb{R}^{4} \) dada por \( F(x, y, z, t)=(\cos (x), y, z, t) \). d) \( F: M_{n \times n} \rightarrow M_{n \times n} \) dada por \( F(X)=X A-A X \), onde \( A_{2 \times 2} \) é uma matriz fixada.

Determine whether the lines L1 and L2 are parallel, skew, or intersecting. L1: x = 12 + 8t, y = 16 − 4t, z = 4 + 12t L2: x = 3 + 12s, y = 9 − 6s, z = 12 + 15s parallel skew intersecting If they intersect, find the point of intersection. (If an answer does not exist, enter DNE.)

Find parametric equations for the line. (Use the parameter t.) the line through (3, 3, 0) and perpendicular to both i + j and j + k x(t), y(t), z(t) = Find the symmetric equations. x + 3 = −(y + 3), z = 0 −(x − 3) = y − 3 = z x − 3 = −(y − 3) = z x + 3 = −(y + 3) = z x − 3 = y − 3 = −z

e) \( 24:(3+9:(4: 2+1))+2:(4+8: 2) \)

Fill in the blanks. If \( c>0,|u|=c \) is equivalent to \( u=\square \) or \( u= \) If \( c>0,|u|=c \) is equivalent to \( u=\square \) or \( u=\square \)